Comparison of long time simulation of Hamilton and Lagrange geometry dynamical models of a multibody system
Long Bai 1,2
Lili Xia 1,2
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Beijing Information Science and Technology University, Mechanical Electrical Engineering School, China
Beijing Information Science and Technology University, School of Applied Science, China
Submission date: 2022-04-12
Final revision date: 2022-07-15
Acceptance date: 2022-09-19
Online publication date: 2022-11-20
Publication date: 2022-11-25
Corresponding author
Long Bai   

Mechanical Electrical Engineering School, Beijing Information Science and Technology University, China
Journal of Theoretical and Applied Mechanics 2022;60(4):687-704
The geometry dynamical modeling method for a double pendulum is explored with the Lie group and a double spherical space method. Four types of Lagrange equations are built for relative and absolute motion with the above two geometry methods, which are then used to explore the influence of different expressions for motion on the dynamic modeling and computations. With Legendre transformation, the Lagrange equations are transformed to Hamilton ones which are dynamical models greatly reduced. The models are solved by the same numerical method. The simulation results show that they are better for the relative group than for the absolute one in long time simulation with the same numerical computations. The Lie group based result is better than the double spherical space one.
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