Generalized Hill's problem - Some cases of complete integrability

Details Generalized Hill's problem - Some cases of complete integrability Generalized Hill's problem - Some cases of complete integrability

Dec 1991

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991cemda..51..363c&link_type=abstract

Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958), vol. 51, no. 4, 1991, p. 363-377.

Mathematics

Dynamical Systems

1

Dynamical Systems, Hill Method, Numerical Integration, Differential Equations, Equations Of Motion, Hamiltonian Functions, Jacobi Integral

Scientific paper

This paper investigates cases of integrability in the planar Hill's problem. The external potential U(ext) is supposed to be time-indepencet in a given uniformly rotating frame. Cases of integrability of the relative motion of two interacting particles in the vicinity of an equilibrium solution of U(ext) are found. In all these cases, the form of the second integral is explicitly given, the first being the Jacobian one. Cases in which the interacting potential U between the two particles is of Newtonian type are particularized.

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