Geometric Pseudospectral Method on Lie Group with application to 3D Pendulum

DOI

10.2991/iccia.2012.262How to use a DOI?

Keywords

geometric pseudospectral method, Lie group, Equivariant map, 3D pendulum

Abstract

General pseudospectral method is extended to Lie group by virtue of equivariant map for solving rigid dynamics on Lie group. In particular, for the problem of structural characteristics of the dynamics system can not be conserved by using general pseudospectral method directly on Lie group, the differential equation evolving on the Lie group is transformed to an equivalent differential equation evolving on a Lie algebra on which general pseudospectral method is used, so that the numerical flow of rigid body dynamics is ensured to stay on Lie group. Furthermore, structural conservativeness and numerical stabilities of this method are validated and analyzed by simulation on a 3D pendulum in comparison with using pseudospectral method directly on Lie group.

Copyright

© 2013, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Jie Li
AU  - Honglei An
AU  - Xueqiang Gu
AU  - Hongtao Xue
PY  - 2014/05
DA  - 2014/05
TI  - Geometric Pseudospectral Method on Lie Group with application to 3D Pendulum
BT  - Proceedings of the 2012 2nd International Conference on Computer and Information Application (ICCIA 2012)
PB  - Atlantis Press
SP  - 1068
EP  - 1073
SN  - 1951-6851
UR  - https://doi.org/10.2991/iccia.2012.262
DO  - 10.2991/iccia.2012.262
ID  - Li2014/05
ER  -