Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Algebraic structure of the manifold of solutions of the $ N$-body problem

Author: Lawrence Goldman
Journal: Proc. Amer. Math. Soc. 25 (1970), 417-422
MSC: Primary 12.80; Secondary 70.00
MathSciNet review: 0260714
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The Theorem of Ritt on the decomposition of the perfect differential ideal generated by a single irreducible differential polynomial is, here, generalized to system of polynomials satisfying certain conditions. We use these results to prove that all solutions of the $ N$-body problem, excepting the solutions for which one or more of the $ {r_{ij}}$ (the distance between the masses $ {M_i},\;{M_j}$) is zero, belong to one irreducible manifold.

References [Enhancements On Off] (What's this?)

  • [1] W. V. D. Hodge and D. Pedoe, Methods of algebraic geometry, Vol. II, Cambridge Univ. Press, Cambridge, 1952. MR 13, 972. MR 1288306 (95d:14002b)
  • [2] E. Leimanis, Some recent advances in the dynamics of rigid bodies and celestial mechanics. Dynamics and nonlinear mechanics, Surveys in Appl. Math., vol. 2, Wiley, New York and Chapman & Hall, London, 1958. MR 20 #2877. MR 0096393 (20:2877)
  • [3] J. F. Ritt, Differential algebra, Amer. Math. Soc. Colloq. Publ., vol. 33, Amer. Math. Soc., Providence, R. I., 1950. MR 12, 7. MR 0035763 (12:7c)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 12.80, 70.00

Retrieve articles in all journals with MSC: 12.80, 70.00

Additional Information

Keywords: Manifold of systems, decomposition of radical ideals, decomposition of perfect differential ideals, Jacobian, $ N$-body problem, three-body problem
Article copyright: © Copyright 1970 American Mathematical Society

American Mathematical Society