The dynamics of rheonomic Lagrangian systems with constraints
General rheonomic Lagrangian systems with non-integrale constraints are considered. Their equations of motion, in the form of the Lagrange equations with multipliers, are equivalent to the variational equation expressing the Hamilton principle in Hölder form, which occurs when determining the synchronous Chetaev variations. A parametric study of the motions of such systems is made in the extended configurational space \({\mathbb{R}}^{n+1}\) with arbitrarily chosen parameters. When the Lagrangian is independent of t and the constraints are homogeneous with respect to the velocities, the equations of motion have an energy integral corresponding to the ignorable coordinate t. The energy integral is used to reduce the order of the initial equations, and a generalization of the Jacobi-Whittaker equations is obtained as a result.
scientific article; zbMATH DE number 3919885