Long Time Simulation Analysis of Geometry Dynamics Model under Iteration

Geometry modeling methods can conserve the geometry characters of a system, which helps the dynamic equations more concisely and is good for long simulations. Reduced attitude, Lie group and Lie algebra are three different expressions of geometry. Models for the dynamics of a planer pendulum and a 3...

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Bibliographic Details
Published in:Applied sciences 2022-05, Vol.12 (10), p.4910
Main Authors: Sun, Weiwei, Bai, Long, Ge, Xinsheng, Xia, Lili
Format: Article
Language:English
Subjects:
Algebra
Coordinate transformations
Differential equations
dynamics
Geometry
geometry mechanical
Lie algebra
lie group
Lie groups
Mechanics
Methods
Newton iteration
Nonlinear equations
Simulation
Simulation analysis
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Summary:Geometry modeling methods can conserve the geometry characters of a system, which helps the dynamic equations more concisely and is good for long simulations. Reduced attitude, Lie group and Lie algebra are three different expressions of geometry. Models for the dynamics of a planer pendulum and a 3D pendulum were built with these three geometry expressions. According to the variation method, the dynamics models as ordinary differential equations were transformed into nonlinear equations which are solved by Newton iteration. The simulation results show that Lie group and Lie algebra calculations can conserve the geometric structure, but have different long-time behavior. The complete Lie group expression has the best long simulation behavior and has the lowest sensitivity to the time step in both planer and 3D pendulum simulations, because it saves the complete geometry of the system in the dynamics model.
ISSN:2076-3417
2076-3417
DOI:10.3390/app12104910