The Rotating Rigid Body Model Based on a Non-twisting Frame

Research output: Contribution to journalArticleResearchpeer review

Authors

  • Cristian Guillermo Gebhardt
  • Ignacio Romero

Research Organisations

External Research Organisations

  • IMDEA Materials Institute
  • Technical University of Madrid (UPM)
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Details

Original languageEnglish
Pages (from-to)3199-3233
Number of pages35
JournalJournal of Nonlinear Science
Volume30
Issue number6
Early online date5 Aug 2020
Publication statusPublished - 1 Dec 2020

Abstract

This work proposes and investigates a new model of the rotating rigid body based on the non-twisting frame. Such a frame consists of three mutually orthogonal unit vectors whose rotation rate around one of the three axis remains zero at all times and, thus, is represented by a nonholonomic restriction. Then, the corresponding Lagrange–D’Alembert equations are formulated by employing two descriptions, the first one relying on rotations and a splitting approach, and the second one relying on constrained directors. For vanishing external moments, we prove that the new model possesses conservation laws, i.e., the kinetic energy and two nonholonomic momenta that substantially differ from the holonomic momenta preserved by the standard rigid body model. Additionally, we propose a new specialization of a class of energy–momentum integration schemes that exactly preserves the kinetic energy and the nonholonomic momenta replicating the continuous counterpart. Finally, we present numerical results that show the excellent conservation properties as well as the accuracy for the time-discretized governing equations.

Keywords

    Conservation laws, Non-twisting frame, Nonholonomic system, Rotating rigid body model, Structure preserving integration

ASJC Scopus subject areas

Cite this

The Rotating Rigid Body Model Based on a Non-twisting Frame. / Gebhardt, Cristian Guillermo; Romero, Ignacio.
In: Journal of Nonlinear Science, Vol. 30, No. 6, 01.12.2020, p. 3199-3233.

Research output: Contribution to journalArticleResearchpeer review

Gebhardt CG, Romero I. The Rotating Rigid Body Model Based on a Non-twisting Frame. Journal of Nonlinear Science. 2020 Dec 1;30(6):3199-3233. Epub 2020 Aug 5. doi: 10.48550/arXiv.1911.03666, 10.1007/s00332-020-09648-3, 10.15488/10545
Gebhardt, Cristian Guillermo ; Romero, Ignacio. / The Rotating Rigid Body Model Based on a Non-twisting Frame. In: Journal of Nonlinear Science. 2020 ; Vol. 30, No. 6. pp. 3199-3233.
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