Details
Original language | English |
---|---|
Pages (from-to) | 3199-3233 |
Number of pages | 35 |
Journal | Journal of Nonlinear Science |
Volume | 30 |
Issue number | 6 |
Early online date | 5 Aug 2020 |
Publication status | Published - 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
- Mathematics(all)
- Modelling and Simulation
- Engineering(all)
- General Engineering
- Mathematics(all)
- Applied Mathematics
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In: Journal of Nonlinear Science, Vol. 30, No. 6, 01.12.2020, p. 3199-3233.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - The Rotating Rigid Body Model Based on a Non-twisting Frame
AU - Gebhardt, Cristian Guillermo
AU - Romero, Ignacio
N1 - Open Access funding provided by Projekt DEAL.
PY - 2020/12/1
Y1 - 2020/12/1
N2 - 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.
AB - 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.
KW - Conservation laws
KW - Non-twisting frame
KW - Nonholonomic system
KW - Rotating rigid body model
KW - Structure preserving integration
UR - http://www.scopus.com/inward/record.url?scp=85089037786&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1911.03666
DO - 10.48550/arXiv.1911.03666
M3 - Article
AN - SCOPUS:85089037786
VL - 30
SP - 3199
EP - 3233
JO - Journal of Nonlinear Science
JF - Journal of Nonlinear Science
SN - 0938-8974
IS - 6
ER -