Lie symmetries and conserved quantities of constrained mechanical systems
The Lie symmetries and conserved quantities of constrained mechanical systems are studied. Using the invariance of the ordinary differential equations under the infinitesimal transformations, the determining equations and the restriction equations of the Lie symmetries of the systems are established. The structure equation and the form of conserved quantities are obtained. We find the corresponding conserved quantity from a known Lie symmetry, that is a direct problem of the Lie symmetries. And then, the inverse problem of the Lie symmetries-finding the corresponding Lie symmetry from a known conserved quantity-is studied. Finally, the relation between the Lie symmetry and the Noether symmetry is given.
KeywordsMechanical System Direct Problem Nonholonomic System Restriction Equation Determine Equation
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