Herglotz-Type Noether Theorem for Nonconservative Nonholonomic System
The Herglotz-type Noether theorem and its inverse theorem for non-conservative nonholonom-ic systems are studied.Firstly,the Herglotz variational principle is extended to non-conservative non-holonomic systems,and the differential equation of motion with multipliers is derived based on this prin-ciple.Secondly,the infinitesimal transformation is introduced to study the invariance of Lagrange-Her-glotz action,and the Noether theorem for non-conservative nonholonomic systems is proposed and proved.Thirdly,the inverse problem of symmetry is studied and Noether's inverse theorem is given.Finally,taking Appell-Hamel problem subject to non-conservative forces as an example,we introduce the application of Herglotz type Noether theorem.
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