INVARIANT-SETS AND SYMMETRICAL PERIODIC MOTIONS OF REVERSIBLE MECHANICAL SYSTEMS

A method of constructing and classifying all symmetric periodic motion s of a reversible mechanical system is proposed. The principal solutio n of the above problem is given for the Hill problem, the restricted t hree-body problem (including the photogravitational problem), the prob lem of a heavy rigid body with a fixed point, and that of a heavy rigi d body on a rough plane. In particular, problems requiring a systemati c numerical study are thereby formulated. (C) 1997 Elsevier Science Lt d.