Generalizations of the Jacobian integral

Details Generalizations of the Jacobian integral Generalizations of the Jacobian integral

Dec 1984

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984cemec..34..125s&link_type=abstract

(Bundesministerium für Wissenschaft und Forschung of Austria, Alexander von Humboldt Colloquium on Celestial Mechanics: The Stab

Physics

3

Celestial Mechanics, Jacobi Integral, Three Body Problem, Equations Of Motion, Gravitational Effects, Lagrangian Equilibrium Points, Orbit Perturbation

Scientific paper

The restricted problem of three bodies is generalized to the restricted problem of 2+n bodies. The system is modified so that there are several gravitationally interacting bodies with small masses. Their motions are influenced by the primaries but they do not influence the motions of the primaries. The separate Jacobian integrals of the minor bodies are lost but a conservative (time-independent) Hamiltonian of the system is obtained. For the case of two minor bodies, the five Lagrangian points of the classical problem are generalized and fourteen equilibrium solutions are established. The four linearly stable equilibrium solutions which are the generalizations of the triangular Lagrangian points are once again stable but only for considerably smaller values of the mass parameter of the primaries than in the classical problem.

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