NDLI: Maxwell Strata and Conjugate Points in the Sub-Riemannian Problem on the Lie Group SH(2)

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Maxwell Strata and Conjugate Points in the Sub-Riemannian Problem on the Lie Group SH(2)

Content Provider	Springer Nature Link
Author	Bhatti, Aamer Iqbal Butt, Yasir Awais Sachkov, Yuri L.
Copyright Year	2016
Abstract	We study local and global optimality of geodesics in the left invariant sub-Riemannian problem on the Lie group SH(2). We obtain the complete description of the Maxwell points corresponding to the discrete symmetries of the vertical subsystem of the Hamiltonian system. An effective upper bound on the cut time is obtained in terms of the first Maxwell times. We study the local optimality of extremal trajectories and prove the lower and upper bounds on the first conjugate times. We also obtain the generic time interval for the n-th conjugate time which is important in the study of sub-Riemannian wavefront. Based on our results of n-th conjugate time and n-th Maxwell time, we prove a generalization of Rolle’s theorem that between any two consecutive Maxwell points, there is exactly one conjugate point along any geodesic.
Ending Page	770
Page Count	24
Starting Page	747
File Format	PDF
ISSN	10792724
e-ISSN	15738698
Journal	Journal of Dynamical and Control Systems
Issue Number	4
Volume Number	22
Language	English
Publisher	Springer US
Publisher Date	2016-04-30
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Geometric methods Systems Theory, Control Conjugate time Optimal control problems involving ordinary differential equations Maxwell points Vibration, Dynamical Systems, Control Sub-Riemannian geometry Special hyperbolic group SH(2) Calculus of Variations and Optimal Control; Optimization Analysis on real and complex Lie groups Analysis Cut time Applications of Mathematics Nonlinear systems
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Control and Systems Engineering Algebra and Number Theory Numerical Analysis

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