On integrability in elementary functions of certain classes of nonconservative dynamical systems
This survey paper integrates the results of the author on mathematics of such mechanical problems as the motion of a body in a resisting medium, being only partially embedded. This kind of problems results in systems with energy dissipation or anti-dissipation (pumping). The main mathematical model turns to be the pendulum second order equation in which there exists a linear dissipative force with variable coefficients which may change sign; in the mean the dissipation may be positive, negative (dispersive forces) or equal to zero - zero mean variable dissipation system (``almost conservative''). For such systems relative ``roughness'' in the sense of Andronov is introduced. The paper discusses zero mean variable dissipation systems with symmetries in both rough and non-rough cases. Systems on the sphere are considered and various phase portraits without limit cycles are presented. Higher order dynamics are considered on Lie algebra \(so(4)\) including symmetries. A comprehensive list of almost 400 references is given.
scientific article; zbMATH DE number 5673498
scientific article