Herglotz-Type Noether Theorem for Vacco Dynamics of Second-Order Nonholonomic Systems
The Herglotz-type Noether theorems for the Vacco dynamics of second-order nonholonomic systems are studied.Firstly,based on the Herglotz generalized variational principle,the Herglotz-type differential equations of motion for Vacco dynamics of second-order nonholonomic systems are established.Secondly,according to the non-isochronous variation formulas of Hamilton-Herglotz action,the concepts of Her-glotz-type Noether symmetry and quasi-symmetry and their criterion equations for Vacco dynamics of second-order nonholonomic systems are given,and the Herglotz-type Noether theorems and their inverse theorems are further derived.Finally,an example is given to illustrate the application of the results.
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