| [1] | T. M. Apostol, CALCULUS volume I One-Variable Calculus, with an Introduction to Linear Algebra, Blaisdell Publishing Company, John Wiley & Sons, 1967. [ bib ] |
| [2] | T. M. Apostol, Calculus, Volume II: Multi-Variable Calculus and Linear Algebra, with Applications to Differential Equations and Probability, John Wiley & Sons, 1969. [ bib ] |
| [3] |
L. K. Babadzhaniants, Existence of the Continuations in the
N-Body Problem, Celestial Mechanics, 20 (1979), pp. 43--57,
https://doi.org/10.1007/BF01236607.
[ bib |
DOI ]
Keywords: Astronomical Models, Celestial Mechanics, Gravitational Effects, Many Body Problem, Extremum Values, Functions (Mathematics), Inequalities, Set Theory, Taylor Series, Astronomy |
| [4] |
L. K. Babadzhanyants, On the global solution of the N-body
problem, Celestial Mechanics and Dynamical Astronomy, 56 (1993),
pp. 427--449, https://doi.org/10.1007/BF00691812.
[ bib |
DOI ]
Keywords: Cauchy Problem, Celestial Mechanics, Many Body Problem, Poincare Problem, Differential Equations, Inertial Reference Systems, Riemann Manifold, Three Body Problem, Transformations (Mathematics), Physics (General), N-body problem, Poincar&eacute, type method, analytic continuation |
| [5] | E. Badolati, On the history of kepler's equation, Vistas in astronomy, 28 (1985), pp. 343--345. [ bib ] |
| [6] | E. Barrabés and S. Mikkola, Families of periodic horseshoe orbits in the restricted three-body problem, Astronomy & Astrophysics, 432 (2005), pp. 1115--1129. [ bib ] |
| [7] | J. Barrow-Green, The dramatic episode of sundman, Historia Mathematica, 37 (2010), pp. 164 -- 203, https://doi.org/https://doi.org/10.1016/j.hm.2009.12.004, http://www.sciencedirect.com/science/article/pii/S0315086009001360. [ bib | DOI | http ] |
| [8] | R. R. Bate, D. D. Mueller, and J. E. White, Fundamentals of astrodynamics, Courier Corporation, 1971. [ bib ] |
| [9] | K. Batygin and M. E. Brown, Evidence for a distant giant planet in the solar system, The Astronomical Journal, 151 (2016), p. 22. [ bib ] |
| [10] | D. Brannan, M. Esplen, and J. Gray-Geometry, Cambrige university press, 1999. [ bib ] |
| [11] | H. Bruns, Über die integrale des vielkörper-problems, Acta Mathematica, 11 (1887), pp. 25--96. [ bib ] |
| [12] | T. Burkardt and J. Danby, The solution of kepler's equation, ii, Celestial Mechanics and Dynamical Astronomy, 31 (1983), pp. 317--328. [ bib ] |
| [13] | J. A. Burns, Elementary derivation of the perturbation equations of celestial mechanics, American Journal of Physics, 44 (1976), pp. 944--949. [ bib ] |
| [14] | S. Chandrasekhar, Newton's Principia for the common reader, Oxford University Press, 2003. [ bib ] |
| [15] | G. E. Christianson and R. S. Westfall, In the presence of the Creator: Isaac Newton and his times, Free Press New York, 1984. [ bib ] |
| [16] | R. Clausius, On a mechanical theorem applicable to heat, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 40 (1870), pp. 122--127. [ bib ] |
| [17] | I. B. Cohen, Newton's Discovery of Gravity, Scientific American, 244 (1981), pp. 166--179, https://doi.org/10.1038/scientificamerican0381-166. [ bib | DOI ] |
| [18] | P. Colwell, Solving kepler's equation over three centuries, Richmond, Va.: Willmann-Bell, 1993., (1993). [ bib ] |
| [19] | B. A. Conway, An Improved Algorithm due to Laguerre for the Solution of Kepler's Equation, Celestial Mechanics, 39 (1986), pp. 199--211, https://doi.org/10.1007/BF01230852. [ bib | DOI ] |
| [20] | G. G. Coriolis, Mémoire sur les équations du mouvement relatif des systèmes de corps, Bachelier, 1835. [ bib ] |
| [21] | J. Danby, The solution of kepler's equation, iii, Celestial mechanics, 40 (1987), pp. 303--312. [ bib ] |
| [22] | J. Danby, Fundamentals of celestial mechanics, Richmond: Willman-Bell,| c1992, 2nd ed., (1992). [ bib ] |
| [23] | J. Danby and T. Burkardt, The solution of kepler's equation, i, Celestial Mechanics, 31 (1983), pp. 95--107. [ bib ] |
| [24] | J. T. Devreese and G. V. Berghe, 'Magic is no magic': the wonderful world of Simon Stevin, WIT Press, 2008. [ bib ] |
| [25] | F. Diacu, The solution of the n-body problem, The mathematical intelligencer, 18 (1996), pp. 66--70. [ bib ] |
| [26] |
P. P. Eggleton, Aproximations to the radii of Roche lobes.,
, 268 (1983), pp. 368--369, https://doi.org/10.1086/160960.
[ bib |
DOI ]
Keywords: Binary Stars, Celestial Mechanics, Orbital Elements, Roche Limit, Mass Ratios, Radii, Astrophysics |
| [27] | H. W. Eves, A Survey of Geometry: Rev. Ed, Allyn and Bacon, 1972. [ bib ] |
| [28] | T. Fukushima, A method solving kepler's equation without transcendental function evaluations, Celestial Mechanics and Dynamical Astronomy, 66 (1996), pp. 309--319. [ bib ] |
| [29] | R. Gavazzi, C. Adami, F. Durret, J.-C. Cuillandre, O. Ilbert, A. Mazure, R. Pello, and M. P. Ulmer, A weak lensing study of the coma cluster, Astronomy & Astrophysics, 498 (2009), pp. L33--L36. [ bib ] |
| [30] | T. Gerkema and L. Gostiaux, A brief history of the coriolis force, Europhysics News, 43 (2012), pp. 14--17. [ bib ] |
| [31] | H. Goldstein, Prehistory of the’’runge--lenz’’vector, American Journal of Physics, 43 (1975), pp. 737--738. [ bib ] |
| [32] | H. Goldstein, More on the prehistory of the laplace or runge-lenz vector, American Journal of Physics, 44 (1976), pp. 1123--1124. [ bib ] |
| [33] | H. Goldstein, C. Poole, and J. Safko, Classical mechanics, 2002. [ bib ] |
| [34] | C. M. Graney, Coriolis effect, two centuries before coriolis, Physics Today, 64 (2011), p. 8. [ bib ] |
| [35] | D. Grebow, Generating periodic orbits in the circular restricted three-body problem with applications to lunar south pole coverage, MSAA Thesis, School of Aeronautics and Astronautics, Purdue University, (2006). [ bib ] |
| [36] | W. R. Hamilton, The hodograph, or a new method of expressing in symbolical language the newtonian law of attraction, in Proceedings of the royal irish academy, vol. 3, 1847, pp. 344--353. [ bib ] |
| [37] | A. C. Hindmarsh, Odepack, a systematized collection of ode solvers, Scientific computing, (1983), pp. 55--64. [ bib ] |
| [38] | J. Horner, N. Evans, M. Bailey, and D. Asher, The populations of comet-like bodies in the solar system, Monthly Notices of the Royal Astronomical Society, 343 (2003), pp. 1057--1066. [ bib ] |
| [39] | E. Julliard-Tosel, Bruns' theorem: The proof and some generalizations, Celestial Mechanics and Dynamical Astronomy, 76 (2000), pp. 241--281. [ bib ] |
| [40] | P. S. Laplace et al., Oeuvres complètes de Laplace, Gautier-Villars, 1835. [ bib ] |
| [41] | R. Meire, An efficient method for solving barker's equation, Journal of the British Astronomical Association, 95 (1985), p. 113. [ bib ] |
| [42] | C. D. Murray and S. F. Dermott, Solar system dynamics, Cambridge university press, 1999. [ bib ] |
| [43] | I. Newton and E. Halley, Philosophiae naturalis principia mathematica, vol. 62, Jussu Societatis Regiae ac typis Josephi Streater, prostant venales apud Sam …, 1780. [ bib ] |
| [44] | A. Nijenhuis, Solving kepler's equation with high efficiency and accuracy, Celestial Mechanics and Dynamical Astronomy, 51 (1991), pp. 319--330. [ bib ] |
| [45] | R. A. Nowlan, Masters of mathematics: The problems they solved, why these are important, and what you should know about them, Springer, 2017. [ bib ] |
| [46] | A. Odell and R. Gooding, Procedures for solving kepler's equation, Celestial mechanics, 38 (1986), pp. 307--334. [ bib ] |
| [47] | H. C. K. Plummer, An introductory treatise on dynamical astronomy, University Press, 1918. [ bib ] |
| [48] | H. Poincaré, Sur le problème des trois corps et les équations de la dynamique, Acta mathematica, 13 (1890), pp. A3--A270. [ bib ] |
| [49] | H. Poincaré, New methods of celestial mechanics, vol. 13, Springer Science & Business Media, 1992. [ bib ] |
| [50] | H. Pollard, A sharp form of the virial theorem, Bulletin of the American Mathematical Society, 70 (1964), pp. 703--705. [ bib ] |
| [51] | H. Pollard, The behavior of gravitational systems, Indiana Univ. Math. J., 17 (1968), pp. 601--611. [ bib ] |
| [52] | J. G. Portilla, Principios de Mecánica Celeste, Universidad Nacional de Colombia, 2019. [ bib ] |
| [53] | W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical recipes 3rd edition: The art of scientific computing, Cambridge university press, 2007. [ bib ] |
| [54] | W. Qiu-Dong, The global solution of the n-body problem, Celestial Mechanics and Dynamical Astronomy, 50 (1990), pp. 73--88. [ bib ] |
| [55] | P. G. Roll, R. Krotkov, and R. H. Dicke, The equivalence of inertial and passive gravitational mass, Annals of Physics, 26 (1964), pp. 442--517. [ bib ] |
| [56] | D. Souami and J. Souchay, The solar system’s invariable plane, Astronomy & Astrophysics, 543 (2012), p. A133. [ bib ] |
| [57] | M. F. Struble and H. J. Rood, A compilation of redshifts and velocity dispersions for aco clusters, The Astrophysical Journal Supplement Series, 125 (1999), p. 35. [ bib ] |
| [58] | K. F. Sundman, Mémoire sur le problème des trois corps, Acta Math., 36 (1913), pp. 105--179, https://doi.org/10.1007/BF02422379, https://doi.org/10.1007/BF02422379. [ bib | DOI | http ] |
| [59] | F. Wilczek, Whence the force of f= ma? i: Culture shock, Physics Today, 57 (2004), pp. 11--12. [ bib ] |
| [60] | A. Wintner, The analytical foundations of celestial mechanics, Dover, 1947. [ bib ] |
| [61] | F. Zwicky, On the Masses of Nebulae and of Clusters of Nebulae, Astrophysical Journal, 86 (1937), p. 217, https://doi.org/10.1086/143864. [ bib | DOI ] |
This file was generated by bibtex2html 1.99.