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A Lie group integrator is a numerical integration method for differential equations built from coordinate-independent operations such as Lie group actions on a manifold. They have been used for the animation and control of vehicles in computer graphics and control systems/artificial intelligence research. These tasks are particularly difficult because they feature nonholonomic constraints.
See also
- Euler integration
- Lie group
- Numerical methods for ordinary differential equations
- Parallel parking problem
- Runge–Kutta methods
- Variational integrator
References
- Celledoni, Elena; Marthinsen, Håkon; Owren, Brynjulf (2012). "An introduction to Lie group integrators -- basics, new developments and applications". Journal of Computational Physics. 257 (2014): 1040–1061. arXiv:1207.0069. Bibcode:2014JCoPh.257.1040C. doi:10.1016/j.jcp.2012.12.031. S2CID 28406272.
- "AN OVERVIEW OF LIE GROUP VARIATIONAL INTEGRATORS AND THEIR APPLICATIONS TO OPTIMAL CONTROL" (PDF).
- Iserles, Arieh; Munthe-Kaas, Hans Z.; Nørsett, Syvert P.; Zanna, Antonella (2000-01-01). "Lie-group methods". Acta Numerica. 9: 215–365. doi:10.1017/S0962492900002154. ISSN 1474-0508. S2CID 121539932.
- "Lie Group Integrators for the animation and control of vehicles" (PDF).
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