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.
We focus on the analysis of this remarkable spectrum, but also
Discuss the atmospheric trajectory, atmospheric penetration, and orbital data
Computed for this bolide which was probably released during
21P/Giacobini-Zinner return to perihelion in 1907. The spectrum is discussed
Together with the tens...
We give sufficient conditions for a contact
Sub-Riemannian manifold with a one-parameter family of symmetries to satisfy
This property. Moreover, in the special case where the quotient of the contact
Sub-Riemannian manifold by the symmetries is Kahler, the sufficient conditions
Are defined by a comb...
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