In this work, we study a class of dissipative, nonsmooth n degree-of-freedom dynamical systems. As the dissipation is assumed to be proportional to the momentum, the dynamics in such systems is conformally symplectic, allowing us to use some of the Hamiltonian structure. We initially show that there exists an integral invariant of the Poincar ́e–Cartan type in such systems. Then, we prove the existence of a generalized Liouville Formula for conformally symplectic systems with rigid constraints using the integral invariant. A two degree-of-freedom system is analyzed to support the relevance of our results.
This work is supported by the National Natural Science Foundation of China (11732014).
The data that support the findings of this study are available within the article.
- Integral invariant
- impact system
- generalized Liouvile Formula