On the existence of periodic solutions of Poincare's second sort in the general problem of three bodies moving in plane

Details On the existence of periodic solutions of Poincare's second sort in the general problem of three bodies moving in plane On the existence of periodic solutions of Poincare's second sort in the general problem of three bodies moving in plane

Jan 1980

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980cemec..21...55m&link_type=abstract

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

Mathematics

7

Celestial Mechanics, Equations Of Motion, Existence Theorems, Poincare Problem, Three Body Problem, Fourier Series, Hamiltonian Functions, Kinetic Energy, Periodic Functions, Potential Energy

Scientific paper

The proof of the general problem of three bodies is offered, which utilizes the symmetry of the equations of motion in an extension of the approach used by Barrar (1965) for the restricted problem. It also uses a device proposed by Poincare which enables the extension to the general problem to be made. Attention is given to the 'Mirror Theorem' of Roy and Ovenden (1955) and to the existence of periodic solutions for small values of epsilon.

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