Seminarium "The Trans-Carpathian Seminar on Geometry & Physics"

We consider the solutions to the Zermelo navigation problem on Riemannian manifolds, under perturbation represented by the weak vector field, in Finsler geometry with application of Randers metric. We compare it to the variational solutions via the Euler-Lagrange equations with non-restricted wind distribution. We focus on the river-type perturbation in the corresponding low-dimensional examples in the context of real applications in navigation. We also propose the geometric modi fication of the standard search patterns in case of acting vector field basing on the time-optimal paths.