DOI: 10.2298/tam260212008p ISSN: 1450-5584
Classification of the geodesic curves of a sub-Riemannian LR system on the Heisenberg group in dimension 5
Milan PavlovicWe study sub-Riemannian structures obtained by the restriction of the standard left-invariant Riemannian metric to a right-invariant completely nonholonomic distribution on the second Heisenberg group. The corresponding Hamiltonian system is completely integrable and we study its solutions in this paper. We obtain a complete classification of the geodesic curves by studying the reduced Hamiltonian system. Moreover, we compute r(t) as the first step of the quadrature in the reduced system in the hyperspherical coordinates and present numerical examples that illustrate the theoretical results.