تقرير
Continuation of Periodic Orbits in Conservative Hybrid Dynamical Systems and its Application to Mechanical Systems with Impulsive Dynamics
| العنوان: | Continuation of Periodic Orbits in Conservative Hybrid Dynamical Systems and its Application to Mechanical Systems with Impulsive Dynamics |
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| المؤلفون: | Raff, Maximilian, Remy, C. David |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Dynamical Systems |
| الوصف: | 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. Comment: re-submitted to Nonlinear Dynamics (August 27, 2024) |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2402.06502 |
| رقم الأكسشن: | edsarx.2402.06502 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |