2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64559We solve a model problem from single crystal plasticity.We consider 4 slip systems in the plane with orthogonal slip-directions and equal slip rates, forward as well as backwards. We compute the associated dissipation distance by solving an optimal control problem. It turns out that from a computational point of view computing the distance is inexpensive. We put special emphasis on visualization of the metric spheres and the associated length-minimizing curves. As a byproduct we also solve a related problem, optimal path planning for a car driving forwards and backwards with limited turning radius in the hyperbolic plane. This is a hyperbolic version of the Reeds-Shepp-Car-Problem first discussed in (Pac. J. Math. 145:367-393, 1990).67 pages, 10 figuresOptimization and ControlMetric Geometry53C22 (Primary) 49Q10 74C15 53A35 (Secondary)text