Lie group integrator explained

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.^{[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

• Euler integration
• Lie group
• Numerical methods for ordinary differential equations
• Parallel parking problem
• Runge–Kutta methods
• Variational integrator

Notes and References

1. 1207.0069. An introduction to Lie group integrators -- basics, new developments and applications. Journal of Computational Physics. 257. 2014. 1040–1061. Celledoni. Elena. Elena Celledoni . Marthinsen. Håkon. Owren. Brynjulf. 2012. 10.1016/j.jcp.2012.12.031. 2014JCoPh.257.1040C. 28406272 .
2. Web site: AN OVERVIEW OF LIE GROUP VARIATIONAL INTEGRATORS AND THEIR APPLICATIONS TO OPTIMAL CONTROL.
3. Iserles. Arieh. Munthe-Kaas. Hans Z.. Nørsett. Syvert P.. Zanna. Antonella. Antonella Zanna . 2000-01-01. Lie-group methods. Acta Numerica. 9. 215–365. 10.1017/S0962492900002154 . 121539932 . 1474-0508.
4. Web site: Lie Group Integrators for the animation and control of vehicles.