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Vol 233, No 3 (2018)
- Year: 2018
- Articles: 2
- URL: https://journals.rcsi.science/1072-3374/issue/view/14945
Article
Low-Dimensional and Multi-Dimensional Pendulums in Nonconservative Fields. Part 2
Abstract
In this review, we discuss new cases of integrable systems on the tangent bundles of finite-dimensional spheres. Such systems appear in the dynamics of multidimensional rigid bodies in non-conservative fields. These problems are described by systems with variable dissipation with zero mean. We found several new cases of integrability of equations of motion in terms of transcendental functions (in the sense of the classification of singularities) that can be expressed as finite combinations of elementary functions.
301-397
Phase Portraits of Dynamical Equations of Motion of a Rigid Body in a Resistive Medium
Abstract
We consider a mathematical model of the influence of a medium on a rigid body with a specific shape of its surface. In this model, we take into account the additional dependence of the moment of the interaction force on the angular velocity of the body. We present a complete system of equations of motion under the quasi-stationarity conditions. The dynamical part of equations of motion forms an independent third-order system, which contains, in its turn, an independent secondorder subsystem. We ovtain a new family of phase portraits on the phase cylinder of quasi-velocities, which differs from families obtained earlier.
398-425