The Inverse Problem of Lie Symmetries of the Nonholonomic Mechanical Systems of Chetaev Type

This paper discusses the inverse problem of lie symmetries of the nonholonomic mechanical systems and finds out the corresponding Lie symmetry on the basis of a known conserved quantity. First, Noether symmetry corresponding to the given conserved quantity needs to be found by Noether theory; second, the symmetry will be examined to see whether it is Lie symmetry or not in light of the determining equations and restriction equations. Furthermore, the nonholonomic mechanical systems with Chetaev's type constraints are studied.