Open AccessEquilibria and oscillations in a reversible mechanical system
Author(s) -
В. Н. Тхай,
AUTHOR_ID
Publication year - 2021
Publication title -
vestnik sankt-peterburgskogo universiteta. matematika. mehanika. astronomiâ/vestnik sankt-peterburgskogo universiteta. seriâ 1, matematika, mehanika, astronomiâ
Language(s) - English
Resource type - Journals
eISSN - 2587-5884
pISSN - 1025-3106
DOI - 10.21638/spbu01.2021.416
Subject(s) - continuation , pendulum , euler's formula , mechanical system , upper and lower bounds , rigid body , classical mechanics , mathematics , physics , control theory (sociology) , mathematical analysis , computer science , quantum mechanics , control (management) , artificial intelligence , programming language
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.