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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.06502 |
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Table of Contents:
- In autonomous differential equations where a single first integral is present, periodic orbits are well-known to belong to one-parameter families, parameterized by the first integral's values. This paper shows that this characteristic extends to a broader class of conservative hybrid dynamical systems (cHDSs). We study periodic orbits of a cHDS, introducing the concept of a hybrid first integral to characterize conservation in these systems. Additionally, our work presents a methodology that utilizes numerical continuation methods to generate these periodic orbits, building upon the concept of normal periodic orbits introduced by Sepulchre and MacKay (1997). We specifically compare state-based and time-based implementations of an cHDS as an important application detail in generating periodic orbits. Furthermore, we showcase the continuation process using exemplary conservative mechanical systems with impulsive dynamics.