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- Article name
- ADVANTAGES OF APPLICATION OF VARIATIONAL INTEGRATORS ON LIE GROUPS IN PROBLEMS OF MODELING THE DYNAMICS OF MECHANICAL SYSTEMS
- Authors
- Moiseev I. S., , ilmoiseev@inbox.ru, Saint-Petersburg State Marine Technical University, Saint-Petersburg, Russia
Zhilenkov A. A., , zhilinkovanton@gmail.com, Saint-Petersburg State Marine Technical University, St. Petersburg, Russia
- Keywords
- Lie groups / variational calculus / variational integrator / modeling / dynamics of mechanical systems
- Year
- 2024 Issue 4 Pages 27 - 34
- Code EDN
- APPLOL
- Code DOI
- 10.52190/1729-6552_2024_4_27
- Abstract
- An algorithm of a variational integrator on Lie groups for modeling the dynamics of a physical pendulum is developed. To compare the variational integrators and the Runge-Kutta method of the 4th order, graphs were constructed showing how the angular velocity along the axes, the orthogonal error, the total energy and the angular momentum change over time. The graphs demonstrate that despite the fact that the angular velocity is the same for both methods, the Runge-Kutta method does not preserve the geometric structure of a continuous system and does not preserve the main constants of the modeled system, namely, mechanical energy and momentum.
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