Название: Numerical solution of a left-invariant sub-Riemannian problem on the group SO(3)
Авторы: D. Stepanov, A. Podobryaev
Журнал: Russian Journal of Nonlinear Dynamics
Год: 2024
Номер: 4
Том: 20
Страницы: 635-670
Образец цитирования:
D.Stepanov, A.Podobryaev. Numerical Solution of a Left-Invariant Sub-Riemannian Problem on the Group SO(3) // Rus. J. Nonlin. Dyn. 20, 4, 635-670 (2024)
Аннотация:
We consider a left-invariant sub-Riemannian problem on the Lie group of rotations of a three-dimensional space. We find the cut locus numerically, in fact we construct the optimal synthesis numerically, i. e., the shortest arcs. The software package nutopy designed for the numerical solution of optimal control problems is used. With the help of this package we investigate sub-Riemannian geodesics, conjugate points, Maxwell points and diffeomorphic domains of the exponential map. We describe some operating features of this software package.