Lie Symmetries and Conserved Quantities of Mechanical Systems of Remainder Coordinates with Unilateral Holonomic Constraints

This paper studies the Lie symmetries and the conserved quantities of unilateral holonomic mechanical systems with remainder coordinates. Using the invariance of ordinary differential equations under the infinitesimal transformations, the author establishes the determining equations, restriction equations, additional restriction equations of the Lie symmetries of the systems and obtains the structure equations and the form of conserved quantities. Meanwhile, the paper discusses the inverse problem of the above, i.e., finding the corresponding Lie symmetry according to a given integral of the systems. In the end of the paper, an example is given to illustrate the application of the results.