A Herglotz-based integrator for nonholonomic mechanical systems

Elias Maciel; Inocencio Ortiz; Christian E. Schaerer; Elias Maciel; Inocencio Ortiz; Christian E. Schaerer

doi:10.3934/jgm.2023012

Journal of Geometric Mechanics

2023, Volume 15, Issue 1: 287-318. doi: 10.3934/jgm.2023012

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Research article

A Herglotz-based integrator for nonholonomic mechanical systems

Polytechnic School - National University of Asuncion, Paraguay

Received: 06 July 2022 Revised: 20 September 2022 Accepted: 20 September 2023 Published: 21 February 2023
Primary: 37M15, 65D30; Secondary: 70G45

We propose a numerical scheme for the time-integration of nonholonomic mechanical systems, both conservative and nonconservative. The scheme is obtained by simultaneously discretizing the constraint equations and the Herglotz variational principle. We validate the method using numerical simulations and contrast them against the results of standard methods from the literature.
- nonholonomic systems,
- nonconservative systems,
- Herglotz principle,
- contact integrator
Citation: Elias Maciel, Inocencio Ortiz, Christian E. Schaerer. A Herglotz-based integrator for nonholonomic mechanical systems[J]. Journal of Geometric Mechanics, 2023, 15(1): 287-318. doi: 10.3934/jgm.2023012

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Abstract

We propose a numerical scheme for the time-integration of nonholonomic mechanical systems, both conservative and nonconservative. The scheme is obtained by simultaneously discretizing the constraint equations and the Herglotz variational principle. We validate the method using numerical simulations and contrast them against the results of standard methods from the literature.

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