## Parametrization of Extremal Trajectories in Sub-Riemannian Problem on Group of Motions of Pseudo Euclidean Plane

arXiv:1305.1338 [math.OC] 6 May 2013

We consider the sub-Riemannian length optimization problem on the group of motions of hyperbolic plane i.e. the special hyperbolic group SH(2). The system comprises of left invariant vector fields with 2 dimensional linear control input and energy cost functional. We prove the global controllability of control distribution and use Pontryagin Maximum Principle to obtain the extremal control input and sub-Riemannian geodesics. The abnormal and normal extremal trajectories of the system are analyzed qualitatively and investigated for strict abnormality. A change of coordinates transforms the vertical subssystem of the normal Hamiltonian system into mathematical pendulum. In suitable elliptic coordinates the vertical and horizontal subsystems are integrated such that the resulting extremal trajectories are parametrized by Jacobi elliptic functions.

Version: za2963e q8zaa q8zb1 q8zc2 q8zdf q8ze4 q8zfa q8zgb

#### Similar articles you may find interesting…

1. H\"older continuity of the value function for control-affine systems

arXiv:1304.6649 [math.OC] 24 Apr 2013

We prove the continuity and we give a Holder estimate for the value function Associated with the $L^1$ cost of the control-affine system $\dot q = \drift(q)+\sum_{j=1}^m u_j f_j(q)$, satisfying the strong H\"ormander Condition. This is done by proving a result in the same spirit as the Ball-Box Theo...
2. Substrate recognition by norovirus polymerase: microsecond molecular dynamics study.
Molecular dynamics simulations of complexes between Norwalk virus RNA dependent RNA polymerase and its natural CTP and 2dCTP (both containing the O5'-C5'-C4'-O4' sequence of atoms bridging the triphosphate and sugar moiety) or modified coCTP (C5'-O5'-C4'-O4'), cocCTP (C5'-O5'-C4'-C4'...
3. Serum biomarkers for neurofibromatosis type 1 and early detection of malignant peripheral nerve-sheath tumors.
Our analysis identified four markers (epidermal growth factor, interferon-gamma, interleukin-6, and tumor necrosis factor-alpha) for which significantly different serum concentrations were seen in patients with NF1 compared with healthy controls. Two markers (insulin-like growth factor binding prote...