Geometric Pseudospectral Method on Lie Group with Application to 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.

• Periodical: Advanced Materials Research (Volumes 756-759)
• Pages: 3021-3029
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.756-759.3021
• Online since: September 2013
• Authors: Jie Li, Hong Lei An, Xue Qiang Gu, Hong Tao Xue
• Keywords: 3D Pendulum, Equivariant Map, Geometric Pseudospectral Method, Lie Group

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