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<p>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&#xa0;(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.</p>

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Continuation of periodic orbits in conservative hybrid dynamical systems and its application to mechanical systems with impulsive dynamics

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年1月23日

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  • Maximilian Raff,
  • C. David Remy

摘要

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.