Accurate conserved quantity and approximate conserved quantity deduced from Noether symmetry for a weakly Chetaev nonholonomic system

Abstract

Accurate conserved quantity and approximate conserved quantity deduced from Noether symmetry of Lagrange equations for a weakly Chetaev nonholonomic system were studied. First, the differential equations of motion of the system were established. Second, under the infinitesimal transformations of group, the definitions of Noether symmetry for the weakly Chetaev nonholonomic system and the first approximate system were given. Third, the first approximate Noether equation was mainly obtained, and the expressions of the accurate and approximate conserved quantities were deduced from the Noether symmetry for the weakly Chetaev nonholonomic system. Finally, an example was given to illustrate the application of the results.

Noether Invariants for Nonholonomic Systems

“…Using foliations, we give here a global form for the invariant objects. The classical setting is as in [10][11][12][13][14][15][16][17][18][19][20][21][22].…”