Lie group integrator

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

References

1. 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.
2. "AN OVERVIEW OF LIE GROUP VARIATIONAL INTEGRATORS AND THEIR APPLICATIONS TO OPTIMAL CONTROL" (PDF).
3. 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.
4. "Lie Group Integrators for the animation and control of vehicles" (PDF).