John Thomas Conway

• Ho, Alex; Wold, Margrethe; Poursina, Mohammad & Conway, John Thomas (2023). The accuracy of mutual potential approximations in simulations of binary asteroids. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 671. doi: 10.1051/0004-6361/202245552. Vis sammendrag

  Context. Simulations of asteroid binaries commonly use mutual gravitational potentials approximated by series expansions, leading to truncation errors, and also preventing correct computations of force and torque for certain configurations where the bodies have overlapping bounding spheres, such as in the rotational fission model for creating asteroid binaries and pairs. Aims. We address errors encountered when potentials truncated at order two and four are used in simulations of binaries, as well as other errors related to configurations with overlapping bounding spheres where the series diverge. Methods. For this we utilized a recently developed method where the gravitational interaction between two triaxial ellipsoids can be calculated without approximations for any configuration. The method utilizes surface integration for both force and torque calculations, and it is exact for ellipsoidal shapes. We also computed approximate solutions using potentials truncated at second and fourth order, and we compare these with the solutions obtained with the surface integral method. The approximate solutions were generated with the “General Use Binary Asteroid Simulator” (GUBAS). Results. If the secondary is located with its centroid in the equatorial plane of the primary, the error in the force increases as the secondary is moved closer to the primary, but is still relatively small for both second and fourth order potentials. For torque calculations, the errors become more significant, especially if the other body is located close to one of the extended principal axes. On the axes themselves, the second order series approximation fails by 100%. For dynamical simulations of components separated a few primary radii apart, the fourth order approximation is significantly more accurate than the second order. Furthermore, because of larger errors in the torque calculations, the rotational motion is subject to greater inaccuracies than the translational motion. For configurations resembling contact binaries where the bounding spheres overlap, the errors in both force and torque in the initial stages of the simulation are considerable, regardless of the approximation order, because the series diverge. A comparison of the computational efficiency of the force and torque calculations shows that the surface integration method is approximately 82 times and four times slower than the second and fourth order potentials, respectively, but approximately 16 times faster than the order eight potential. Comparing the computation efficiency of full simulations, including the calculations of the equations of motion, shows that the surface integration scheme is comparable with GUBAS when an order four potential is used. Conclusions. The errors generated when mutual gravitational potentials are truncated at second or fourth order lead to larger errors in the rotational than in the translational motion. Using a mathematically exact method for computing forces and torques becomes important when the bodies are initially close and the bounding spheres overlap, in which case both the translational and rotational motion of the bodies have large errors associated with them. For simulations with two triaxial ellipsoids, the computational efficiency of the surface integral method is comparable to fourth order approximations with GUBAS, and superior to eight order or higher.

• Ho, Alex; Wold, Margrethe; Poursina, Mohammad & Conway, John Thomas (2022). Dynamics of asteroid systems post-rotational fission. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 665. doi: 10.1051/0004-6361/202243706. Fulltekst i vitenarkiv
• Conway, John Thomas (2021). Indefinite integrals from Wronskians for Whittaker and Gauss hypergeometric functions. Integral transforms and special functions. ISSN 1065-2469. doi: 10.1080/10652469.2021.2011864.
• Ho, Alex; Wold, Margrethe; Conway, John Thomas & Poursina, Mohammad (2021). Extended two-body problem for rotating rigid bodies. Celestial mechanics & dynamical astronomy. ISSN 0923-2958. 133. doi: 10.1007/s10569-021-10034-8. Fulltekst i vitenarkiv Vis sammendrag

  A new technique that utilizes surface integrals to find the force, torque and potential energy between two non-spherical, rigid bodies is presented. The method is relatively fast, and allows us to solve the full rigid two-body problem for pairs of spheroids and ellipsoids with 12 degrees of freedom. We demonstrate the method with two dimensionless test scenarios, one where tumbling motion develops, and one where the motion of the bodies resemble spinning tops. We also test the method on the asteroid binary (66391) 1999 KW4, where both components are modelled either as spheroids or ellipsoids. The two different shape models have negligible effects on the eccentricity and semi-major axis, but have a larger impact on the angular velocity along the z-direction. In all cases, energy and total angular momentum is conserved, and the simulation accuracy is kept at the machine accuracy level.

• Conway, John Thomas (2021). Indefinite integrals from Wronskians and related linear second-order differential equations. Integral transforms and special functions. ISSN 1065-2469. doi: 10.1080/10652469.2021.1938025. Fulltekst i vitenarkiv
• Wold, Margrethe & Conway, John Thomas (2021). The planar two-body problem for spheroids and disks. Celestial mechanics & dynamical astronomy. ISSN 0923-2958. 133. doi: 10.1007/s10569-021-10023-x. Fulltekst i vitenarkiv
• Conway, John Thomas (2021). Indefinite integrals involving the exponential integral function. Integral transforms and special functions. ISSN 1065-2469. doi: 10.1080/10652469.2021.1893718. Fulltekst i vitenarkiv
• Conway, John Thomas (2020). Indefinite Integrals involving Jacobi polynomials from integrating factors. Integral transforms and special functions. ISSN 1065-2469. doi: 10.1080/10652469.2020.1844197.
• Conway, John Thomas (2020). Indefinite integrals for some orthogonal polynomials obtained using integrating factors. Integral transforms and special functions. ISSN 1065-2469. doi: 10.1080/10652469.2020.1786382. Fulltekst i vitenarkiv
• Conway, John Thomas (2020). A third integrating factor for indefinite integrals of special functions. Integral transforms and special functions. ISSN 1065-2469. doi: 10.1080/10652469.2020.1777115. Fulltekst i vitenarkiv
• Conway, John Thomas (2020). A generalized integration formula for indefinite integrals of special functions. Integral transforms and special functions. ISSN 1065-2469. 31(8), s. 586–600. doi: 10.1080/10652469.2020.1721485. Fulltekst i vitenarkiv
• Conway, John Thomas (2019). Indefinite integrals of special functions from integrating factors. Integral transforms and special functions. ISSN 1065-2469. doi: 10.1080/10652469.2019.1689567.
• Conway, John Thomas (2019). Indefinite Integrals of special functions from hybrid equations. Integral transforms and special functions. ISSN 1065-2469. s. 1–15. doi: 10.1080/10652469.2019.1686630.
• Conway, John Thomas (2019). More indefinite integrals from Riccati equations. Integral transforms and special functions. ISSN 1065-2469. 30(12), s. 1004–1017. doi: 10.1080/10652469.2019.1647538.
• Conway, John Thomas (2018). Indefinite integrals of special functions from inhomogeneous differential equations. Integral transforms and special functions. ISSN 1065-2469. 30(3), s. 166–180. doi: 10.1080/10652469.2018.1548014.
• Conway, John Thomas (2018). New indefinite integrals from a method using Riccati equations. Integral transforms and special functions. ISSN 1065-2469. 29(12), s. 927–941. doi: 10.1080/10652469.2018.1525368.
• Conway, John Thomas (2018). New special function recurrences giving new indefinite integrals. Integral transforms and special functions. ISSN 1065-2469. 29(10), s. 805–819. doi: 10.1080/10652469.2018.1499099.
• Conway, John Thomas (2018). Indefinite integrals of quotients of Gauss hypergeometric functions. Integral transforms and special functions. ISSN 1065-2469. 29(6), s. 417–430. doi: 10.1080/10652469.2018.1451527.
• Conway, John Thomas (2018). Indefinite integrals of quotients of special functions. Integral transforms and special functions. ISSN 1065-2469. 29(4), s. 269–283. doi: 10.1080/10652469.2018.1428582.
• Conway, John Thomas (2017). Mutual inductance of thick coils for arbitrary relative orientation and position, Progress in Electromagnetics Research Symposium, PIERS-FALL 2017. IEEE conference proceedings. ISSN 978-1-5386-1211-8. s. 1388–1395. doi: 10.1109/PIERS-FALL.2017.8293347.
• Conway, John Thomas (2017). Indefinite integrals involving the Jacobi Zeta and Heuman Lambda functions. Integral transforms and special functions. ISSN 1065-2469. 28(8), s. 576–589. doi: 10.1080/10652469.2017.1330335.
• Conway, John Thomas (2017). Indefinite integrals involving complete elliptic integrals of the third kind. Integral transforms and special functions. ISSN 1065-2469. 28(6), s. 488–503. doi: 10.1080/10652469.2017.1315415.
• Conway, John Thomas (2017). Indefinite integrals of incomplete elliptic integrals from Jacobi elliptic functions. Integral transforms and special functions. ISSN 1065-2469. 28(6), s. 443–459. doi: 10.1080/10652469.2017.1304938.
• Conway, John Thomas (2016). Indefinite integrals of products of special functions. Integral transforms and special functions. ISSN 1065-2469. 28(3), s. 166–180. doi: 10.1080/10652469.2016.1259619.
• Conway, John Thomas (2016). Vector potentials for the gravitational interaction of extended bodies and laminas with analytical solutions for two disks. Celestial mechanics & dynamical astronomy. ISSN 0923-2958. 125(2), s. 161–194. doi: 10.1007/s10569-016-9679-y.
• Conway, John Thomas (2016). Indefinite integrals involving the incomplete elliptic integral of the third kind. Integral transforms and special functions. ISSN 1065-2469. 27(8), s. 667–682. doi: 10.1080/10652469.2016.1184662.
• Conway, John Thomas (2016). Indefinite integrals involving the incomplete elliptic integrals of the first and second kinds. Integral transforms and special functions. ISSN 1065-2469. 27(5), s. 371–384. doi: 10.1080/10652469.2015.1132715.
• Conway, John Thomas (2016). Indefinite integrals of Lommel functions from an inhomogeneous Euler–Lagrange method. Integral transforms and special functions. ISSN 1065-2469. 27(3), s. 197–212. doi: 10.1080/10652469.2015.1110818.
• Conway, John Thomas (2015). A Lagrangian method for deriving new indefinite integrals of special functions. Integral transforms and special functions. ISSN 1065-2469. 26(10), s. 812–824. doi: 10.1080/10652469.2015.1052807.
• Conway, John Thomas (2015). Indefinite integrals of some special functions from a new method. Integral transforms and special functions. ISSN 1065-2469. 26(11), s. 845–858. doi: 10.1080/10652469.2015.1063627.
• Conway, John Thomas (2014). Analytical solution from vector potentials for the gravitational field of a general polyhedron. Celestial mechanics & dynamical astronomy. ISSN 0923-2958. 121(1), s. 17–38. doi: 10.1007/s10569-014-9588-x.
• Conway, John Thomas (2013). Forces Between Thin Coils With Parallel Axes Using Bessel Functions. IEEE transactions on magnetics. ISSN 0018-9464. 49(9), s. 5028–5034. doi: 10.1109/TMAG.2013.2251652. Vis sammendrag

  A method based on Bessel functions is presented for calculating the forces between combinations of thin coils with parallel axes. The coaxial case is solved in closed form in terms of elliptic integrals, whereas for the noncoaxial case the force components are expressed both as integrals of Bessel functions and as integrals of complete elliptic integrals. The results for the coaxial case have been compared with calculations in the literature with excellent agreement. The numerical results presented for the noncoaxial have been cross-checked by comparing the two methods. These methods can also be applied to current loops, disk coils, thick noncoaxial cylindrical coils, and various combinations, sometimes giving closed-form solutions.

• Conway, John Thomas (2013). Analytical and Semi-Analytical Solutions for the Force Between Circular Loops in Parallel Planes. IEEE transactions on magnetics. ISSN 0018-9464. 49(8), s. 4817–4823. doi: 10.1109/TMAG.2013.2245912. Vis sammendrag

  Closed-form solutions are presented for the force between noncoaxial coplanar circular current loops. A semi-analytical solution is given for the case where the loops lie in parallel planes. Numerical results are given which cross check these solutions against each other and against an independently developed method. The closed form solution for the force between a circular loop and a coaxial circular arc segment is also given.

• Conway, John Thomas (2013). Analytical solutions for the self- and mutual inductances of concentric coplanar disk coils. IEEE transactions on magnetics. ISSN 0018-9464. 49(3), s. 1135–1142. doi: 10.1109/TMAG.2012.2229287. Vis sammendrag

  In this paper, closed-form solutions are presented for the self- and mutual inductances of disk coils which lie concentrically in a plane. The solutions are given as generalized hypergeometric functions which are closely related to elliptic integrals. The method used is a Legendre polynomial expansion of the inductance integral, which renders all integrations straightforward. Excellent numerical agreement with previous studies is obtained. An asymptotic formula for the approach to the ring coil limit is also derived and numerically validated. The methods presented here can be applied to noncoaxial and noncoplanar cases.

• Conway, John Thomas (2012). Exact Solutions for the Mutual Inductance of Circular Coils and Elliptic Coils. IEEE transactions on magnetics. ISSN 0018-9464. 48(1), s. 81–94. doi: 10.1109/TMAG.2011.2161768. Vis sammendrag

  An exact solution is presented for the mutual inductance between general noncoaxial thin circular and elliptic coils with parallel axes. The thin coil solution is given as an angular integral of an elliptic integral expression. In addition, for the coaxial case, an exact solution is given for the mutual inductance of a thick circular coil and a thick elliptic coil. The elliptic coil is such that the coil thickness is the same along both elliptic semi-axes. The thick coil solution is given as an integral of an expression involving Bessel and Struve functions. Extensive numerical results for sample geometries are given for both solutions, which are cross checked against each other in the limit as the thick coils become thin.

• Conway, John Thomas (2012). Non coaxial force and inductance calculations for Bitter coils and coils with uniform radial current distributions. Journal of Applied Superconducivity and Electromagnetics. ISSN 1836-7151. 3(1), s. 61–64. doi: 10.1109/asemd.2011.6145068.
• Conway, John Thomas (2011). Non Coaxial Force and Inductance Calculations for Bitter Coils and Coils with Uniform Radial Current Distributions, Proceedings of 2011 IEEE International Conference on Applied Superconductivity and Electromagnetic Devices Sydney, Australia, December 14-16,2011. IEEE conference proceedings. ISSN 9781424478514. s. 61–64. Vis sammendrag

  Recently the Bessel function approach to calculating the magnetic fields of coils has been used to calculate the mutual inductance and the force between two non coaxial thick cylindrical coils with parallel axes and uniform radial current distributions. This method can also be applied to calculate the force and inductance between an ordinary coil and a Bitter coil, or between two bitter coils, not necessarily coaxial. Bitter coils give a simpler case of the method, and it is possible to solve analytically for the magnetic field of a bitter disk.

• Conway, John Thomas (2011). Mutual inductance for an explicitly finite number of turns. Progress in Electromagnetics Research B. ISSN 1937-6472. 28, s. 273–287. doi: 10.2528/PIERB1011010. Vis sammendrag

  Non coaxial mutual inductance calculations, based on a Bessel function formulation, are presented for coils modelled by an explicitly ¯nite number of circular turns. The mutual inductance of two such turns can be expressed as an integral of a product of three Bessel functions and an exponential factor, and it is shown that the exponential factors can be analytically summed as a simple geometric progression, or other related sums. This allows the mutual inductance of two thin solenoids to be expressed as an integral of a single analytical expression. Sample numerical results are given for some representative cases and the approach to the limit where the turns are considered to be smeared out over the solenoid windings is explored.

• Conway, John Thomas (2011). Geometric efficiency for a circular detector and a ring source of arbitrary orientation and position. Nuclear Instruments and Methods in Physics Research Section A : Accelerators, Spectrometers, Detectors and Associated Equipment. ISSN 0168-9002. 640(1), s. 99–109. doi: 10.1016/j.nima.2011.03.014.
• Conway, John (2010). Geometric efficiency for a circular detector and a linear source of arbitrary orientation and position. Nuclear Instruments and Methods in Physics Research Section A : Accelerators, Spectrometers, Detectors and Associated Equipment. ISSN 0168-9002. 622(3), s. 555–566. doi: 10.1016/j.nima.2010.07.068. Vis sammendrag

  A new axisymmetric radiation vector potential which is singular along its entire axis of symmetry is derived for a spherically symmetric point radiation source. This potential and a previously given non-singular point source potential are integrated to give radiation vector potentials for a straight linear source of constant strength. Analytical solutions are given for the geometric efficiency G of a line source and a circular disk detector when the line source is parallel to the detector axis. The analytical solution is also given for the case where the line source is parallel to the disk surface, such that the source axis and the detector axis intersect. All other cases are given as simple one-dimensional trigonometric integrals. Numerical results for G are given for all cases considered, and results given previously by Pomme for a line source parallel to the detector plane have been verified. The methods and vector potentials presented here can be adapted for calculations with many different geometries, and many results are applicable in other fields such as electromagnetism, gravity and fluid mechanics.

• Conway, John & Cohl, Howard S. (2010). Exact Fourier expansion in cylindrical coordinates for the three-dimensional Helmholtz Green function. Zeitschrift für Angewandte Mathematik und Physik. ISSN 0044-2275. 61(3), s. 425–443. doi: 10.1007/s00033-009-0039-6. Vis sammendrag

  A new method is presented for Fourier decomposition of the Helmholtz Green function in cylindrical coordinates, which is equivalent to obtaining the solution of the Helmholtz equation for a general ring source. The Fourier coefficients of the Green function are split into their half advanced + half retarded and half advanced-half retarded components, and closed form solutions for these components are then obtained in terms of a Horn function and a Kamp, de F,riet function respectively. Series solutions for the Fourier coefficients are given in terms of associated Legendre functions, Bessel and Hankel functions and a hypergeometric function. These series are derived either from the closed form 2-dimensional hypergeometric solutions or from an integral representation, or from both. A simple closed form far-field solution for the general Fourier coefficient is derived from the Hankel series. Numerical calculations comparing different methods of calculating the Fourier coefficients are presented. Fourth order ordinary differential equations for the Fourier coefficients are also given and discussed briefly.

• Conway, John (2010). Analytical solution for the solid angle subtended at any point by an ellipse via a point source radiation vector potential. Nuclear Instruments and Methods in Physics Research Section A : Accelerators, Spectrometers, Detectors and Associated Equipment. ISSN 0168-9002. 614(1), s. 17–27. doi: 10.1016/j.nima.2009.11.075. Vis sammendrag

  An axially symmetric radiation vector potential is derived for a spherically symmetric point source. This vector potential is used to derive a line integral for the solid angle subtended at a point source by a detector of arbitrary shape and location. An equivalent line integral given previously by Asvestas for optical applications is derived using this formulation. The line integral can be evaluated in closed form for important cases, and the analytical solution for the solid angle subtended by an ellipse at a general point is presented. The solution for the ellipse was obtained by considering sections of a right elliptic cone. The general solution for the ellipse requires the solution of an auxiliary cubic equation, but simpler formulas are possible for special cases. Numerical results both from the analytical formulas and direct numerical integration are given. The solution for the ellipse also provides exact solutions for the magnetic field of an elliptical current loop and the velocity field of a thin elliptical vortex. The well known solid angle formulas for a circular disk are also derived using this formulation.

• Conway, John (2010). Inductance Calculations for Circular Coils of Rectangular Cross Section and Parallel Axes Using Bessel and Struve Functions. IEEE transactions on magnetics. ISSN 0018-9464. 46(1), s. 75–81. doi: 10.1109/TMAG.2009.2026574. Vis sammendrag

  A simple method for calculating the mutual and self inductances of circular coils of rectangular cross section and parallel axes is presented. The method applies to non-coaxial as well as coaxial coils, and self inductance can be calculated by considering two identical coils which coincide in space. It is assumed that current density is homogeneous in the coil windings. The inductances are given in terms of one-dimensional integrals involving Bessel and Struve functions, and an exact solution is given for one of these integrals. The remaining terms can be evaluated numerically to great accuracy using computer packages such as Mathematica. The method is compared with other exact methods for the coaxial case, and with a filamentary method for the non-coaxial case. Excellent agreement was found in all cases, and the exact method presented here agrees with another exact coaxial method to great numerical accuracy.

• Conway, John (2008). Noncoaxial inductance calculations without the vector potential for axisymmetric coils and planar coils. IEEE transactions on magnetics. ISSN 0018-9464. 44(4), s. 453–462. doi: 10.1109/TMAG.2008.917128. Vis sammendrag

  This paper presents an exact method for calculating the mutual inductance between a general axisymmetric coil and a second planar coil consisting of either a disk coil or a planar loop of essentially arbitrary shape. The approach is based directly on the magnetic field B rather than the vector potential A. The paper gives detailed results for two circular loops, a circular loop and an elliptic loop, and a circular loop and an annular disk coil. The method can be extended to cover the cases where all these loops and coils are extruded in the axial direction to give the corresponding solenoids. The method is also applicable to calculations for nuclear radiation detectors.

• Conway, John (2008). Calculations for a disk source and a general detector using a radiation vector potential. Nuclear Instruments and Methods in Physics Research Section A : Accelerators, Spectrometers, Detectors and Associated Equipment. ISSN 0168-9002. 589(1), s. 20–33. doi: 10.1016/j.nima.2008.02.017. Vis sammendrag

  A closed form expression for a radiation vector potential is derived for a generalized disk radiation source. By applying Stokes's theorem the surface integral for the radiation flux into a general detector is converted into a much simpler line integral of the vector potential around the edge of the detector. This line integral can be easily evaluated for general detector geometry and general location and angular orientation relative to the disk source. For a number of cases the line integral reduces to integrals of Bessel functions which give various generalizations of Ruby's formula. Explicit formulas and numerical results for the geometric efficiency are given for circular and elliptical detectors displaced and rotated relative to the disk source. Detectors with general polygonal boundaries are considered and formulas and sample numerical results are given. For uniform surface emissivity the corresponding formulas for a disk detector and a general planar source are easily obtained. Formulas are also obtained for a scalar radiation potential and some limitations for its applicability are identified. (c) 2008 Elsevier B.V. All rights reserved.

• Conway, John (2008). Fourier series for elliptic integrals and some generalizations via hypergeometric series. Integral transforms and special functions. ISSN 1065-2469. 19(5), s. 305–315. doi: 10.1080/10652460701855898. Vis sammendrag

  Fourier series are derived for generalizations of the three canonical Legendre incomplete elliptic integrals using a hypergeometric series approach. The Fourier series for the incomplete Epstein - Hubbell integrals are obtained as special cases of the generalization of the Legendre integrals of the first and second kinds. The Fourier series for the integrals of the first and second kinds, and those for the Epstein - Hubbell integrals, were obtained recently using a different approach, but the series obtained for the generalization of the incomplete integral of the third kind is new. All cases of the integral of the third kind are given, with the modulus and the parameter being complex variables, and the Fourier coefficients are given in terms of the Kampe de Feriet function for all cases.

• Conway, John (2007). Geometric efficiency for a parallel-surface source and detector system with at least one axisymmetric surface. Nuclear Instruments and Methods in Physics Research Section A : Accelerators, Spectrometers, Detectors and Associated Equipment. ISSN 0168-9002. 583(02.mar), s. 382–393. Vis sammendrag

  An exact and numerically friendly method is given to calculate the geometric efficiency G of a planar radiation source and cosine detector system. Either the source or the detector, but not necessarily both, must have axial symmetry. For two non-coaxial disks the results are in exact agreement with a recent generalization of Ruby's formula for G. Detailed formulas and sample numerical results are given for a disk combined with rectangles and triangles. A disk and a general polygon can be solved by dividing the polygon into triangles. The method can also be applied to electrical inductance calculations and a solution recently given for the inductance of circular and elliptic loops can be directly applied to the corresponding source/detector calculation. All formulas give G=0.5 exactly in the limit of a very large detector.

• Conway, John (2007). Fourier and other series containing associated Legendre functions for incomplete Epstein-Hubbell integrals and functions related to elliptic integrals. Integral transforms and special functions. ISSN 1065-2469. 18(3), s. 179–191. Vis sammendrag

  Fourier series containing associated Legendre functions are given for functions related to the Legendre elliptic integrals and for incomplete Epstein-Hubbell integrals. A number of definite and indefinite integrals related to these series are derived. Additional series of Legendre functions and integrals are derived from a binomial expansion of the reciprocal of the delta amplitude. A power series expansion for the elliptic integral of the third kind in terms of the parameter a is obtained. Series of associated Legendre functions are given for general monomials.

• Conway, John (2007). Inductance calculations for noncoaxial coils using Bessel functions. IEEE transactions on magnetics. ISSN 0018-9464. 43(3), s. 1023–1034. Vis sammendrag

  A relatively simple and general. method for calculating the mutual inductance and self-inductance of both coaxial and noncoaxial cylindrical coils is given. For combinations of cylindical coils, thin solenoids, pancake coils, and simple circular loops, the mutual inductance can be reduced to a one-dimensional integral of closed form expressions involving Bessel and related functions. Coaxial and noncoaxial cases differ only by the presence of an extra Bessel factor J(o) (sp) in the noncoaxial integral, where p is the perpendicular distance separating the coil axes and s is the variable of integration. The method is related to a recently given noncoaxial generalization of Ruby's formula for a nuclear radiation source and detector system, the analogy being close but not exact. In many cases, the Bessel function integral for the inductance can be easily evaluated directly using Maple or Mathematica. In other cases, it is better to transfor in the integral to a more numerically friendly form. A general analytical solution is presented for the inductance of two circular loops which lie in the same plane.

• Conway, John (2006). Fourier series for the Legendre elliptic integrals. Integral transforms and special functions. ISSN 1065-2469. 17(7), s. 499–505. Vis sammendrag

  Simple Fourier series in terms of the amplitude phi are derived for the common Legendre elliptic integrals. The coefficients in the various series contain Legendre functions of the second kind and half-integral degree, also known as toroidal functions. For the Legendre elliptic integrals of the first and second kinds, F (phi, k ) and E (phi, k ), repectively, the expansions given are simple sine series in the amplitude phi and an additional aperiodic term proportional to phi. These series are valid for phi is an element of r. The complete elliptic integral of the third kind Pi(alpha(2), k ) can be expressed in terms of Heumans lambda function Lambda(0)(beta, k ) and the Jacobi zeta function Z (beta, k), which in turn can be expressed in terms of the integrals of the first and second kinds. This enables simple sine series in terms of beta to be derived for Lambda(0)(beta,k ) and Z(beta,k ). The series for Lambda(0)(beta,k ) has an aperiodic term in beta but the series for Z(beta,k ) does not. The various series are obtained by first expanding the delta amplitude and Delta(-1) (phi, k ) as cosine series in the amplitude phi and integrating term by term with repect to phi. The recurrence relation for the Legendre functions is frequently used to simplify or rearrange the various series.

• Conway, John (2006). Generalizations of Ruby's formula for the geometric efficiency of a parallel-disk source and detector system. Nuclear Instruments and Methods in Physics Research Section A : Accelerators, Spectrometers, Detectors and Associated Equipment. ISSN 0168-9002. 562(1), s. 146–153. Vis sammendrag

  Ruby's formula for a parallel-disk source and detector system has been generalized to include non-coaxial disks and a source disk with an arbitrary radial distribution of surface emissivity. The results in all cases are given as one-dimensional integrals of products of Bessel functions and exponentials. For the case of coaxial disks, the solution can always be expressed in closed form as a sum of complete elliptic integrals. For the coaxial case with constant emissivity treated by Ruby, the solution is also given as a simple numerically friendly angular integral. (c) 2006 Elsevier B.V. All rights reserved. Ruby's formula for a parallel-disk source and detector system has been generalized to include non-coaxial disks and a source disk with an arbitrary radial distribution of surface emissivity. The results in all cases are given as one-dimensional integrals of products of Bessel functions and exponentials. For the case of coaxial disks, the solution can always be expressed in closed form as as a sum of complete elliptic integrals. For the coaxial case with constant emissivity treated by Ruby, the solution is also given as a simple numerically friendly angular integral.

• Conway, John (2006). Trigonometric integrals for the magnetic field of the coil of rectangular cross section. IEEE transactions on magnetics. ISSN 0018-9464. 42(5), s. 1538–1548. Vis sammendrag

  Formulas are derived giving the vector potential and the magnetic field components of a general coil of rectangular cross section and constant winding density. The solution is given in a cylindrical coordinate system in terms of trigonometric integrals. The formulas presented have been cross-checked and validated against alternative expressions giving the various field components as integrals of expressions containing Bessel and Struve functions. The trigonometric integrals for the fields can be evaluated easily to several hundred significant figures using mathematical packages such as Maple or Mathematica. Alternatively, they can be evaluated with a small FORTRAN program. Sample results and field line plots obtained with the method are given, and the field of a coil of rectangular cross section is examined in some detail. A comparison with the results of a finite-element method is also given.

• Conway, John (2006). Epstein-Hubbell integrals regarded as associated Legendre functions of the second kind. Radiation Physics and Chemistry. ISSN 0969-806X. 75(4), s. 453–462. Vis sammendrag

  The Epstein-Hubbell integrals were introduced by Hubbell et al. [1961. Radiation field from a circular disk source. J. Res. Nat. Bur. Stand. 65(C), 249-264] in the context of calculations on radiation from a circular disk source. Papers by Hubbell and Epstein [1963. Evaluation of a generalized elliptic-type integral. J. Res. Nat. Bur. Stand. 67(B), 1-17] and Weiss [1964. A note on a generalized elliptic integral. J. Res. Nat. Bur. Stand. 68(B), 1-2] then examined these integrals from the mathematical point of view. In recent years considerable attention has been given to working out the various mathematical properties of these functions, and to devising various generalizations of them. Here it is shown that apart from a simple algebraic factor, the Epstein-Hubbell integrals are associated Legendre functions of the second kind and half-integral degree, also known as toroidal functions. Hence many of the results developed for Legendre functions can be immediately applied to Epstein-Hubbell integrals, and many of the various properties worked out over the years follow more or less immediately from the Legendre function connection, together with some new results. One of the generalizations devised for the Epstein-Hubbell integrals stands out as most natural in this context. (c) 2006 Elsevier Ltd. All rights reserved.

• Conway, John (2005). New exact solution procedure for the near fields of the general thin circular loop antenna. IEEE Transactions on Antennas and Propagation. ISSN 0018-926X. 53(1), s. 509–517. Vis sammendrag

  An analytical method is presented which gives the various fields, including the scalar potential, of a general circular loop antenna in cylindrical coordinates in terms of six separate series. Three of the series are elementary and the other three involve Legendre functions of the second kind and half-integral order. The results obtained are compared with direct numerical integration and with two far-field formulae; the standard textbook expression and what appears to be a new formula which gives more accurate results. The series solution is more robust than numerical integration for the higher Fourier terms of the general solution close to the loop. The solution has also been compared with the solution of Werner, and it agrees exactly. The solution presented here gives better convergence close to the loop, whereas Werner's solution is better far from the loop. Sample calculations are given for the axisymmetric case.

• Conway, John & Su, Jichao (2003). PMAL Flow Calculations for the Aurora Aircraft Using Non-axisymmetric Propeller Actuator Disks. Canadian Aeronautics and Space Journal. ISSN 0008-2821. 49(1), s. 1–9. Vis sammendrag

  A non-axisymmetric actuator disk model has been implemented in the PMAL panel method to assess the effect of a non-axisymmetric slipstream on the aerodynamics of the Aurora aircraft. Perhaps the model's single greatest advantage is that it is simple touse and can be applied to any panel method without any geometry or case-dependent wake stitching. In the current model, the slipstream is swept along the free-stream direction, but it is anticipated that in future developments the effects of the flow fields induced by the aircraft and the propellers themselves on slipstream position will be taken into account by an iterative inviscid coupling between PMAL and the propeller model. Alternatively, if the slipstream position is experimentally known, thiscan be directly input to the model. Since the propeller disk is rotated relative to the slipstream direction, due to incidence and sideslip, the slipstream appears to be of approximately elliptic cross section when viewed along the slipstream direction. However, when viewed perpendicular to the propeller axis, the slipstream consists of a sheared distribution of circular vortex disks, which can be modelled using elliptic integrals. The axisymmetric slipstream contraction has been applied to the calculations, which preserves this circular disk cross section in planes normal to the propeller axis. Results are presented here for cases at incidence and with both incidence and yaw for the cruise value of the thrust coefficient based on disk area (CTh=0.1) and also for a very high thrust coefficient of CTh=2.958. For these cases it has been assumed that the loads on the propeller disks are axisymmetric even though the slipstream is not. The results for the cruise thrust coefficient cases show littlechange from those obtained from an axisymmetric slipstream model. For the high thrust coefficient cases, the results are also not much more complex than for the earlier axisymmetric slipstream model. The surface-pressure distributions for sideslip cases strongly resemble those obtained for cases without sideslip

• Conway, John (2001). Exact Solutions for the Magnetic Fields of Axisymmetric Solenoids and Current Distributions. IEEE transactions on magnetics. ISSN 0018-9464. 37(4), s. 2977–2988. Vis sammendrag

  An analytical method originally developed for fluid mechanics has been applied to the analogous problem of calculating the magnetic field induced by axisymmetric current sheets, disks and solenoids. The magnetic fields of a generalized axisymmetric current distribution are given either in closed form as elliptic integral expressions or as integrals of elementary functions over a finite range. The paper concentrates on the analysis of the fields generated by specified current distributions, though the method can also be applied to solve boundary problems.

• Su, Jichao & Conway, John (2001). Numerical Analysis of the Aerodynamics of the Aurora Aircraft by an Inviscid/Viscous Interaction Method. Canadian Aeronautics and Space Journal. ISSN 0008-2821. 47(1), s. 17–24. Vis sammendrag

  The PMAL3D computer code has been extended to an aircraft configuration with propellers by embedding a nonlinear actuator disk theory developed by Conway (1998)in the PMAL3D inviscid/viscous interaction code developed at AL/IAR/NRC. The theory of the panel method, integral boundary layer method, and the actuator disk model are briefly presented in this paper. This study has included both propeller and viscous effects on the aerodynamics of an aircraft and presented detailed numerical analyses and discussions of the aerodynamics for the Aurora configuration.

• Schaffarczyk, A. Peter & Conway, John (2000). Comparison of a Nonlinear Actuator Disk Theory with Numerical Integration Including Viscous Effects. Canadian Aeronautics and Space Journal. ISSN 0008-2821. s. 209–215. Vis sammendrag

  The nonlinear inviscid actuator disk theory of Conway has been compared with a numerical solution of the Navier-Stokes equations for the equivalent disk discontinuity problem in the presence of viscosity. Good agreement between these two different approaches was obtained, confirming that viscous effects are small for the isolated disk, which has no solid boundaries and hence does not have a no-slip boundary condition.

• Conway, John (2000). Exact solutions for the gravitational potential of a family of heterogeneous spheroids. Monthly notices of the Royal Astronomical Society. ISSN 0035-8711. 316(3), s. 555–558. Vis sammendrag

  An infinite family of heterogeneous spheroids has been found for which exact or closed-form solutions for the Newtonian gravitational potential can be given. The family includes both axisymmetric spheroids and spheroids where the matter density varies harmonically with the azimuthal angle. For the axisymmetric family of spheroids, which have no azimuthal dependence of the density, the potential external to the spheroid is of the same form as the potential exterior to a spheroidal homoeoid. It is therefore constant on the surface of the spheroid and on all external spheroidal surfaces confocal with it. The potential is also constant on all internal confocal spheroidal surfaces, with the value on each confocal surface dependent on the density distribution chosen. However, the density is not constant on either concentric or confocal spheroids. These solutions can be considered to be generalizations of analogous spherical solutions given in a companion paper by Conway. For the classical solutions for homogeneous spheroids, the surface is not equipotential, and these are not included within the new family of solutions, except in the sp

• Conway, John (2000). Analytical solutions for the Newtonian gravitational field induced by matter within axisymmetric boundaries. Monthly notices of the Royal Astronomical Society. ISSN 0035-8711. 316(3), s. 540–554. Vis sammendrag

  An analytical method originally applied to the problem of the actuator disc in fluid mechanics has been applied to the closely analogous problem of constructing the classical Newtonian potential and attractions. The method can treat axisymmetric problems and also non-axisymmetric cases where matter is confined within axisymmetric boundaries. The potential and attractions for the generalized thin finite disc can be given in closed form in terms of elliptic integrals and elementary functions. For the general case of matter within an axisymmetric boundary, the potentials and attractions can be evaluated as one-dimensional integrals of albeit complex analytical expressions. These expressions represent the fields induced by matter in an extended region as a distribution of gravitating discs. For certain special cases, such as matter bounded by a circular cylinder and also for matter distributed in a spherical region, closed-form solutions can be given that appear to be new. Some non-axisymmetric results are also given for the thin disc of infinite radial extent.

• Conway, John & Su, Jichao (2000). PMAL Propeller-Induced Asymmetric Flow Calculations for the Aurora Aircraft Using Embedded Non-Linear Actuator Disks. ?. 46(1), s. 20–27. Vis sammendrag

  An inviscidly exact nonlinear actuator disk model for non-uniform loading has been developed and embedded in the three-dimensional PMAL panel method. The method gives predictions of the time-averaged induced velocities in the slipstream of a propeller with a hub which compare very well with experiment. Predictions of thrust-torque characteristics also agree well with balance data. The method has been applied to the Aurora maritime surveillance aircraft to assess the asymmetry induced by the four propellers rotating in the same sense.

• Conway, John (1998). Prediction of the Performance of Heavily Loaded Propellers with Slipstream Contraction. Canadian Aeronautics and Space Journal. ISSN 0008-2821. 44(3), s. 169–174. Vis sammendrag

  A method of solving exactly for the inviscid flow induced by a heavily loaded propeller actuator disk with nin-uniform distribution of load along the blades has been developed. The method is based on the discretization of the slipstream vorticity into axi-symmetric "vortex disks" rather than the usual concentric vortex sheets. The flow induced by a vortex disk with arbitrary radial distribution of vorticity can be expressed analytically in terms of complete elliptic integrals and the complete flow field can therefore be obtained by numerical integration of these analytical expressions. For a specified blade loading the slipstream boundary and the vorticity distribution in the slipstream are determined iteratively. The exact solution for the induced axial velocity at the actuator disk agrees closely with the Glauert theory for light loading but but gives quite different predictions for heavy loading. The actuator disk theory can be combined with blade element theory to relate the load distribution along the blades to the propeller geometry for specified operating conditions.

• Conway, John (1998). Exact actuator disk solutions for non-uniform heavy loading and slipstream contraction. Journal of Fluid Mechanics. ISSN 0022-1120. 365, s. 235–267. Vis sammendrag

  A semi-analytical method has been developed to solve for the inviscid incompressible flow induced by a heavily loaded actuator disk with non-uniform loading. The solution takes the contraction of the slipstream fully into account. The method is an extension of the analytical theory of conway (1995) for the linearized actuator disk and is exact for an incompressible perfect fluid. The solutions for the velocities and stream function are given as one-dimensional integrals of expressions containing complete elliptic integrals. Any load distribution with bounded radial gradient can be treated. Results are presented here for both contra-rotating and normal propellers. For the special case of a contra-rotating propeller with a parabolic velocity profile in the ultimate wake, the vorticity in the slipstream is shown to be the same as in the analytically tractable spherical vortex of Hill (1894) and the related family of steady vortices explored by Fraenkel (1970, 1972) and Norbury (1973).

• Conway, John (1995). Analytical solutions for the actuator disk with variable radial distribution of load. Journal of Fluid Mechanics. ISSN 0022-1120. 297, s. 327–355. Vis sammendrag

  An analytical method somewhat analogous to finite wing theory has been developed which enables the flow induced by a linearized propeller actuator disk with variable radial distribution of load to be solved in closed form for the first time. Analytical solutions are given for various load distributions including the case of an arbitrary polynomial loading. As in finite wing theory, the case of elliptic loading is exceptionally simple and the induced velocities and stream function are simple expressions of elementary functions. Results are also given for a practical propeller load distribution with finite hub. The method can also be used to solve a wide range of analogous electromagnetic problems.

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• Wold, Margrethe; Ho, Alex; Poursina, Mohammad & Conway, John Thomas (2022). Two-body interactions with surface integrals.
• Ho, Alex; Wold, Margrethe; Conway, John Thomas & Poursina, Mohammad (2021). Dynamics of Asteroid Binary Systems through the Use of Surface Integrals.
• Wold, Margrethe; Conway, John Thomas & Ho, Alex (2019). The planar rigid two-body problem.
• Conway, John Thomas (2018). A Lagrangian method for deriving new indefinite integrals of special functions. I Jahr, Ernst Håkon; Nossum, Rolf Tomas; Thygesen, Ragnar & Breen, Olav (Red.), Agder Vitenskapsakademi, Årbok 2017. Portal forlag. ISSN 978-82-02-59723-8. s. 53–78.
• Conway, John Thomas (2017). Mutual Inductance of Thick Coils for Arbitrary Relative Orientation and Position.
• Conway, John Thomas (2013). Exact Axisymmetric Solutions for the Magnetic Force Between Disk Coils.
• Conway, John Thomas (2011). Exact solution for the force between thick circular and elliptical coils.
• Conway, John (2008). Lecture on propellers and wind turbines. Vis sammendrag

  Lecture given at the Fachhochschule Kiel, Germany, on 2nd December 2008. Presented the actuator disk theory of propellers and wind turbines to masters students in renewable energy.

• Conway, John (2004). Cylindrical Green's Function Approach For Wind Turbines and Related Applications.
• Conway, John & Schaffarczyk, A. Peter (2003). Comparison of Actuator Disk Theory With Navier-Stokes Calculations for a Yawed Actuator Disk.
• Conway, John (2003). Analytical Solutions for the General Non-Axisymmetric Linearized Actuator Disk AIAA 2003-3521. Vis sammendrag

  Previous axisymmetric solutions for the linearized actuator disk have been extended to the non-axisymmetric case by solving for all three components of the vector potential of the flow. When the free-stream is directed along the disk axis, the general non-axisymmetric solution can be given in closed form on terms of elliptic integrals or elementary functions. For the disk at incidence and/or sideslip, the general solution is given as a one-dimensional integral of closed-form expressions, representing the inductions of a sheared distribution of vortex disks. Analytical and numerical results are presented for sample cases. The method can be easily embedded in a boundary integral method to calculate the flow induced by the propellers of an aircraft configuration.

• Conway, John (2002). Application of an Exact Nonlinear Actuator Disk Theory to Wind Turbines. Vis sammendrag

  A nonlinear actuator disk theory has been developed for aircraft propellers which provides an exact solution for the incompressible Euler equations. The paper applies these to the closely related wind turbine case. The method is based on representing the vortex wake of the turbine as a distribution of axisymmetric "vortex disks". A feature of the method is that it allows for the variation of load along the turbine blades. The paper focuses on the nonlinear phenomena found near the maximum power condition of the turbine, and their effect on the maximum possible power coefficient. Various radial load distributions are explored.

• Conway, John (2002). Application of an Exact Nonlinear Actuator Disk Theory to Wind Turbines. Vis sammendrag

  A nonlinear actuator disk theory has been developed for aircraft propellers which provides an exact solution for the incompressible Euler equations. The paper applies these to the closely related wind turbine case. The method is based on representing the vortex wake of the turbine as a distribution of axisymmetric "vortex disks". A feature of the method is that it allows for the variation of load along the turbine blades. The paper focuses on the nonlinear phenomena found near the maximum power condition of the turbine, and their effect on the maximum possible power coefficient. Various radial load distributions are explored.

• Conway, John & Tezok, Fatih (2001). Unsteady three-dimensional vortex sheet panel solutions for oscillating wings. Vis sammendrag

  The paper describes the application of the CANAERO-T panel method to the problem of wings oscillating in pitch. The method has already been applied to impulsively started cases. CANAERO-T models inviscid unsteady flow around complex configurations using constant source panels on the configuration surface and bilinear doublet distributions on wake panels and on the camber surfaces of lifting components. Neumann boundary conditions are applied on the configuration surface and wake convection is used to compute the development with time of the wakes. Pressure distributions and forces are calculated from the unsteady Bernoulli equation, with the time-derivative of the potential calculated using central differencing of the solutions for 3 consecutive time-steps. The method is able to capture the nonlinear self-interaction of the wake as it propagates downstream from the trailing edges of the lifting components, showing the "mushrooming" effect previously reported for two-dimensional calculations. The paper examines wing cases at high and low reduced frequency and hysteresis and phaze effects are explored.

• Conway, John & Tezok, Fatih (2000). Unsteady Three-dimensional Vortex Sheet Panel Solutions for Oscillating Wings.
• Su, Jichao & Conway, John (2000). Numerical Analysis of the Aerodynamics of the Aurora Aircraft by an Inviscid/Viscous Interaction Method. Vis sammendrag

  The PMAL3D computer code has been extended to an aircraft configuration with propellers by embedding a nonlinear actuator disk theory developed by Conway in the PMAL3D inviscid/viscous interaction code developed at AL/IAR/NRC. The actuator disk model was coupled to PMAL3D by introducing the time-averaged velocity field induced by each propeller actuator disk as a modification of the free stream. The theory of the panel method and the actuator disk model are briefly presented in the present paper. This study has included both propeller and viscous effects on the aerodynamics of an aircraft and presented detailed numerical analyses and discussions of the aerodynamics of the Aurora configuration.

• Tezok, Fatih & Conway, John (2000). Calculation of Unsteady Incompressible Inviscid Flow About Wings and Bodies Using The CANAERO-T Panel Model. Vis sammendrag

  The paper describes the unsteady aero/hydrodynamic loads and wake shapes obtained by the CANAERO-T three dimensional panel program developed at Canadair. CANAERO-T is a low order, Time-stepping panel method modelling the unsteady potential flow around a configuration using linear source panels on the surfaces and bi-linearly varying doublet panel distributions in the wake and along the camber surfaces. The paper describes the implementation and testing of the CANAERO-T unsteady code, and describes the mathematical formulation of the method, some features of which appear to be unique.

• Conway, John (2000). Prediction of the Performance of Heavily Loaded Propellers with Slipstream Contraction. Vis sammendrag

  A method of solving exactly for the inviscid flow induced by a heavily loaded propeller actuator disk with non-uniform distribution of load along the blades has been developed. The method is based on the discretization of the slipstream vorticity into axi-symmetric "vortex disks" rather than the usual concentric vortex sheets. The flow induced by a vortex disk with arbitrary radial distribution of vorticity can be expressed analytically in terms of complete elliptic integrals and the complete flowfield can therefore be obtained by numerical integration of these analytical expressions. For a specified blade loading the slipstream boundary and the vorticity distribution in the slipstream are obtained iteratively. The exact solution for the induced axial velocity at the actuator disk agrees closely with Glaurt theory for light loading but gives quite different predictions for heavy loading. The actuator disk theory can be combined with blade element theory to relate the load distribution along the blades to the propeller geometry for specified operating conditions.

• Conway, John & Su, Jichao (2000). PMAL Propeller-Induced Asymmetric Flow Calculations for the AURORA Aircraft Using Embedded Nonlinear Actuator Disks. Vis sammendrag

  An inviscidly exact nonlinear actuator disk model for non-uniform loading has been developed and embedded in the three-dimensional PMAL panel method. The method gives predictions of the time-averaged induced velocities in the slipstream of a propeller with a hub which compare very well with experiment. Predictions of thrust-torque characteristics also agree well with balance data. The method has been applied to the Aurora maritime surveillance aircraft to assess the asymmetry induced by the four propellers rotating in the same sense.

• Conway, John & Tezok, Fatih (2000). A Time-Marching Scheme for the CANAERO Three-Dimensional Vortex Sheets Panel Method. Vis sammendrag

  This paper describes the extension of the CANAERO vortex sheet panel method into the time domain by time-marching with wake convection. Results are given for various generic configurations such as impulsively started wings and wing combinations, and oscillating wings. The method is able to handle the close approach of wakes to downstream lifting surfaces and appears to show considerable promise for calculation of the interaction of tightly coupled lifting surfaces.

• Ho, Alex; Wold, Margrethe; Poursina, Mohammad & Conway, John Thomas (2023). Modeling asteroid binary systems with the full two-body problem using surface integrals. Universitetet i Agder. ISSN 978-82-8427-149-1. Fulltekst i vitenarkiv Vis sammendrag

  An asteroid binary system, where two asteroids are in mutual orbit, is important to study as it can provide knowledge of the history of the asteroid population. The most important mechanism to form asteroid binaries in the near-Earth population, and for asteroids with diameters less than 10 km, is rotational fission. Rotational fission occurs when a rubble pile asteroid, which can be thought of as a collection of rocks held together by gravity, reaches a critical spin rate and the rubble pile starts to shed mass. Studying the dynamics of asteroid binaries allows one to better understand how they have evolved. However, due to their non-spherical shapes, one has to take into account both the translational and rotational motion of asteroids, which is known as the full two-body problem. The study of the full two-body problem is a challenge as the mutual gravitational potential between two non-spherical bodies cannot be expressed analytically. Previous studies have used approximations to model the mutual potential between two asteroids. However, these approximations often suffer from inaccuracies when the bodies are close to each other, and also from truncation errors. In this thesis, we make use of a new method to determine the mutual potential, between two asteroids, with the use of surface integrals. We apply this method to study the dynamics of the 1999 KW4 binary system, where both bodies are modeled as ellipsoids. With the use of an order nine Runge-Kutta method, the system energy and angular momentum are conserved to the 11th decimal digit. One of the advantages of the surface integration method is that the results are valid even if the bodies are close to each other. We make use of this advantage to study the dynamics of asteroid systems formed by rotational fission, as the two bodies are very close to each other in the initial formation stages. We consider ellipsoidal bodies for the simulations. Six models are considered, three where the secondary takes different densities and three where we change the shape of the secondary. The simulations show that more than 80\% of the simulations result in the two bodies colliding. The secondary is more likely to escape the gravitational pull of the primary, forming an asteroid pair, and experience secondary fission, if the secondary has a higher density than the primary, or has a more elongated shape. We also compare the rotation periods of the bodies from the simulations with the ones from observations of asteroid binaries and pairs. The rotation periods from the simulations match very well with the rotation periods of observed asteroid pairs. The surface integration scheme can yield exact values to the mutual gravitational potential between two ellipsoidal bodies. This method can therefore be used to determine the accuracy of methods that approximates the mutual potential between two ellipsoids. We compare the surface integration scheme with an approach that expands the mutual potential with the use of inertia integrals. The differences in the gravitational force and torque, between the two methods, are less than 1\% if the bodies are separated by $2-3$ times the radius of the primary. If the bodies are almost touching, however, the differences can exceed 100\% if the shape of the primary becomes elongated. The discrepancies in the torques are typically an order magnitude larger than the difference in the forces.

• Conway, John Thomas; Federico, F; Stewart, K; Campbell, M; Krogstad, Unni & Stevens, Donna [Vis alle 7 forfattere av denne artikkelen] (2014). God håndtering av alvorlige, uønskede hendelser i helsetjenesten. Nasjonalt kunnskapssenter for helsetjenesten. ISSN 978-82-8121-900-7. Fulltekst i vitenarkiv
• Conway, John (2001). Ph.D. in Applied Mathematics under the Special regulations.
• Conway, John (1994). Analytic Solution of the Flow Induced by a Propeller Actuator Disk for Arbitrary Radial Loading Using Integral Transform Techniques. Agder ingeniør og distriktshøgskole. Vis sammendrag

  An analytical method somewhat analogous to finite wing theory has been developed which enables the flow induced by a linearized propeller actuator disk with arbitary radial loading to be solved in closed form for the first time. Analytical solutions are presented for various load distributions including the case of an arbitrary polynomial loading. As in finite wing theory, the case of elliptic loading is exceptionally simple and the induced velocities and stream function are simple expressions of elementary functions. The flow induced by any propeller can be given in closed form by representing the blade load distribution as a polynomial in the radial coordinate. The method can also solve a wide range of analogous electromagnetic problems.

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