Reduction for constrained variational problems on 3D null curves

Details Reduction for constrained variational problems on 3D null curves Reduction for constrained variational problems on 3D null curves

2007-10-02

arxiv.org/abs/0710.0483v1

SIAM J. Control Optim. 47 (2008) 1399-1414

Mathematics

Differential Geometry

16 pages

Scientific paper

10.1137/070686470

We consider the optimal control problem for null curves in de Sitter 3-space defined by a functional which is linear in the curvature of the trajectory. We show how techniques based on the method of moving frames and exterior differential systems, coupled with the reduction procedure for systems with a Lie group of symmetries lead to the integration by quadratures of the extremals. Explicit solutions are found in terms of elliptic functions and integrals.

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