Open AccessOn exact solutions of equations of rotational motion of a rigid body under action of torque of circular-gyroscopic forces
Author(s) -
А. А. Косов,
Е. И. Семенов
Publication year - 2021
Publication title -
žurnal srednevolžskogo matematičeskogo obŝestva
Language(s) - English
Resource type - Journals
eISSN - 2587-7496
pISSN - 2079-6900
DOI - 10.15507/2079-6900.23.202102.159-170
Subject(s) - action (physics) , moment of inertia , mathematics , rigid body , mathematical analysis , classical mechanics , inertia , torque , equations of motion , rotation around a fixed axis , angular velocity , motion (physics) , polynomial , gyroscope , nonlinear system , differential equation , limit (mathematics) , physics , quantum mechanics , thermodynamics
. A nonlinear system of differential equations describing the rotational motion of a rigid body under the action of torque of potential and circular-gyroscopic forces is considered. For this torque, the system of differential equations has three classical first integrals: the energy integral, the area integral, and the geometric integral. For the analogue of the Lagrange case, when two moments of inertia coincide and the potential depends on one angle, an additional first integral is found and integration in quadratures is performed. A number of examples is considered where parametric families of exact solutions are considered. In these examples, polynomial or analytical functions were used as a potential. In particular, we construct families of periodic and almost periodic motions, as well as families of asymptotically uniaxial rotations. We also identified movements that have limit values of opposite signs for unlimited increase and decrease of time.