Equilibria and oscillations in a reversible mechanical system

Abstract

The paper investigates symmetric periodic motions (SPM) of reversible mechanical systems. A solution is given to the problem of bilateral continuation of a nondegenerate SPM to the global family of such SPMs. The result is applied to the general case of Euler’s problem on a heavy rigid body, when the body parameters are not bound by equality conditions and two families of pendulum oscillations are found connecting the lower and upper equilibria.