Lie group integrator
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A Lie group integrator is a numerical integration method for differential equations built from such as Lie group actions on a manifold.[1][2][3] They have been used for the animation and control of vehicles in computer graphics and control systems/artificial intelligence research.[4] These tasks are particularly difficult because they feature nonholonomic constraints.
See also[]
- Lie group
- Numerical methods for ordinary differential equations
- Euler integration
- Runge–Kutta methods
- Variational integrator
- Parallel parking problem
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.
- ^ "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. ISSN 1474-0508.
- ^ "Lie Group Integrators for the animation and control of vehicles" (PDF).
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