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

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).

Manifolds (Glossary)

Basic concepts

Main results (list)

Types of
manifolds

Vectors	Distribution Lie bracket Pushforward Tangent space bundle Torsion Vector field Vector flow
Covectors	Closed/Exact Covariant derivative Cotangent space bundle De Rham cohomology Differential form Vector-valued Exterior derivative Interior product Pullback Ricci curvature flow Riemann curvature tensor Tensor field density Volume form Wedge product
Bundles	Adjoint Affine Associated Cotangent Dual Fiber (Co) Fibration Jet Lie algebra (Stable) Normal Principal Spinor Subbundle Tangent Tensor Vector
Connections	Affine Cartan Ehresmann Form Generalized Koszul Levi-Civita Principal Vector Parallel transport

Related

Generalizations

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