Lie symmetries and conserved quantites of holonomic systems in phase space

摘要

The Lie symmetries and conserved quantities of holonomic systems in phase space are studied. Using the invariance of the ordinary differential equations under the infinitesimal transformations, the Lie symmetric determining equations of the dynamical equations in phase space are established. The structure equations and the form of the conserved quantities are obtained. An example to illustrate the application of the result is given.