Invariant sets and polhodes in the rigid body problem

Details Invariant sets and polhodes in the rigid body problem Invariant sets and polhodes in the rigid body problem

Jan 1980

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980cemec..21...45l&link_type=abstract

(Conference on Mathematical Methods in Celestial Mechanics, 6th, Oberwolfach, West Germany, Aug. 14-19, 1978.) Celestial Mechani

Mathematics

1

Celestial Mechanics, Many Body Problem, Rigid Structures, Set Theory, Angular Momentum, Euler Equations Of Motion, Invariance, Kinetic Energy, Lie Groups, Three Body Problem

Scientific paper

Sets in the rigid body phase space are described where the energy and angular momentum are constant. The concept of a pinched cell bundle is generalized to examine the invariant subsets of the planar n-body problem. The problem of Smale's (1970) study of the planar n-body problem and Easton's study (1971) of the planar three-body problem are discussed exemplifying in particular the central force problem. The methods are extended to give results for generalized solids on Lie groups, mentioning the further extensions to transitive mechanical systems.

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