On Time-Dependent Lagrangian Systems over Lie Groups and Variational Integrators
DOI:
https://doi.org/10.70567/mc.v42.ocsid8576Keywords:
Lagrangian systems, Lie groups, Time-dependent Lagrangian systems, Variational integratorsAbstract
Time-dependent Lagrangian mechanical systems are of great interest in various branches of engineering and physics. In particular, in robotics, many non-autonomous, that is time-dependent Lagrangian systems, are considered. In this work, we present the dynamics of such systems on Lie groups, considering both continuous and discrete time variables. Within this framework, we address the problem of integrating their equations of motion using discrete variational techniques. We illustrate the approach with simple examples whose configuration space is the Euclidean group, and propose their discrete counterparts. We also study an example on the group of spatial rotations, and finally discuss future research directions aimed at developing variational integrators for more general systems.
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