Reduction, Relative Equilibria and Potential in the Two Rigid Bodies Problem

Details Reduction, Relative Equilibria and Potential in the Two Rigid Bodies Problem Reduction, Relative Equilibria and Potential in the Two Rigid Bodies Problem

Mar 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995cemda..63....1m&link_type=abstract

Celestial Mechanics & Dynamical Astronomy, Volume 63, Issue 1, pp.1-28

Astronomy and Astrophysics

Astronomy

36

Rigid Bodies, Reduction, Relative Equilibria

Scientific paper

In this paper the problem of two, and thus, after a generalization, of an arbitrary finite number, of rigid bodies is considered. We show that the Newton-Euler equations of motion are Hamiltonian with respect to a certain non-canonical structure. The system possesses natural symmetries. Using them we shown how to perform reduction of the number of degrees of freedom. We prove that on every stage of this process equations of motion are Hamiltonian and we give explicite form corresponding of non-canonical Poisson bracket. We also discuss practical consequences of the reduction. We prove the existence of 36 non-Lagrangean relative equilibria for two generic rigid bodies. Finally, we demonstrate that our approach allows to simplify the general form of the mutual potential of two rigid bodies.

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