This article is cited in 7 papers

MECHANICS

Equilibria and oscillations in a reversible mechanical system

V. N. Tkhai

Institute of Control Sciences of the Russian Academy of Sciences, 65, Profsoyuznaya ul., Moscow, 117997, Russian Federation

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.

Keywords: reversible mechanical system, equilibrium, symmetric periodic motion, continuation, global family, Euler's problem, pendulum oscillations.

UDC: 517.93:531.36

MSC: 70H33, 34C25, 70E17

Received: 28.03.2021
Revised: 02.06.2021
Accepted: 17.07.2021

DOI: 10.21638/spbu01.2021.416

 English version: Vestnik St. Petersburg University, Mathematics, 2021, 8:4, 447–451