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Periodic motions in systems with viscous frictionтезисы доклада
- Авторы: Kugushev E., Selezneva M., Shahova T.
- Сборник: 16th International Conference "Dynamical Systems – Theory and Applications". Abstracts
- Тезисы
- Год издания: 2021
- Место издания: Politechnika Łódzka Łódz
- Первая страница: 139
- Последняя страница: 140
- DOI: 10.34658/9788366741201
- Аннотация: An autonomous dissipative system with one degree of freedom in the presence of asmall parameter is considered. It is proved that for sufficiently small values of the parameter in such a system there is a unique limit cycle, it is stable, its period smoothly depends on the small parameter. We apply this theory to several certain systems. The problem of motion of a rigid body (tripod or monopod) freely rotating around a fixed vertical axis and leaning on a horizontal plane with isotropic or anisotropic linear viscous friction uniformly rotating around a fixed vertical axis is considered. If the distance between the axes of rotation of the supporting plane and the rigid body is small enough, then the rigid body asymptotically goes into the unique periodic mode of motion. For both models of friction the dependence of the period of the limit cycle on the small distance between the axes of rotation of the plane and the rigid body is explored analytically. An approximate formula connecting this period and the coefficients of friction in the isotropic and anisotropic cases is found. Numerical simulation of the researched systems is carried out and it is shown that the analytically found dependence for the period can be used to determine the parameters of the viscous friction models.
- Добавил в систему: Шахова Татьяна Валентиновна