Abstract
In this paper we study geodesics of a left-invariant sub-Riemannian metric on a three-dimensional solvable Lie group. A system of differential equations for geodesics is derived from Pontryagin maximum principle and by using Hamiltonian structure. In a generic case the normal geodesics are described by elliptic functions, and their qualitative behavior is quite complicated.
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Mazhitova, A.D. Sub-riemannian geodesics on the three-dimensional solvable non-nilpotent lie group solv− . J Dyn Control Syst 18, 309–322 (2012). https://doi.org/10.1007/s10883-012-9145-4
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DOI: https://doi.org/10.1007/s10883-012-9145-4