Lie group integrator
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Short description: Method of numerical integration of partial differential equations
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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.[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
- ↑ 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. doi:10.1016/j.jcp.2012.12.031. Bibcode: 2014JCoPh.257.1040C.
- ↑ "AN OVERVIEW OF LIE GROUP VARIATIONAL INTEGRATORS AND THEIR APPLICATIONS TO OPTIMAL CONTROL". http://www.math.ucsd.edu/~mleok/pdf/mleok_scicade07.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. https://www.cambridge.org/core/journals/acta-numerica/article/liegroup-methods/856125FF1EAF7762DEF6E37EEBA9CA5F.
- ↑ "Lie Group Integrators for the animation and control of vehicles". https://www.cs.cmu.edu/~kmcrane/Projects/LieGroupIntegrators/paper.pdf.
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