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- Title
Herglotz-type principle and first integrals for nonholonomic systems in phase space.
- Authors
Dong, Xin-Chang; Zhang, Yi
- Abstract
The Herglotz-type principle and first integrals in phase space for nonconservative nonholonomic systems are researched. Firstly, we focus on Herglotz-type first integrals for generalized Chaplygin systems. For nonconservative generalized Chaplygin systems in phase space, we establish differential variational principle of Herglotz type and derive the transformation of principle's invariance condition. Then conservation theorem with corresponding inverse theorem of the system is established, and Herglotz-type Noether first integrals are given. Secondly, we investigate Herglotz-type first integrals for general nonholonomic systems and establish the differential variational principle of Herglotz type for general nonholonomic systems in phase space; then, the conservation theorem and corresponding inverse theorem based on principle's invariance conditions are obtained. Further, Herglotz-type Noether first integrals are presented. Finally, taking generalized Chaplygin system with nonconservative forces and Appell–Hamel problem as examples, their Herglotz Noether first integrals are given by using the theorems we obtained.
- Subjects
NONHOLONOMIC dynamical systems; PHASE space; GENERALIZED integrals; INTEGRALS; VARIATIONAL principles
- Publication
Acta Mechanica, 2023, Vol 234, Issue 12, p6083
- ISSN
0001-5970
- Publication type
Article
- DOI
10.1007/s00707-023-03707-y