A connection theoretic approach to sub-Riemannian geometry
Copyright policy )A connection theoretic approach to sub-Riemannian geometry
We use the notion of generalized connection over a bundle map in order to present an alternative approach to sub-Riemannian geometry. Known concepts, such as normal and abnormal extremals, will be studied in terms of this new formalism. In particular, some necessary and sufficient conditions for the existence of abnormal extremals will be derived. We also treat the problem of characterizing those curves that verify both the nonholonomic equations and the so-called vakonomic equations for a `free' particle submitted to some kinematical constraints.
accepted for publication in J. Geom. Phys
- Ghent University Belgium
nonholonomic mechanics, Mathematics - Differential Geometry, connections, Sub-Riemannian geometry, sub-Riemannian geometry, Differential Geometry (math.DG), Optimization and Control (math.OC), 53C05, 53C17, 58E25, Applications of variational problems to control theory, FOS: Mathematics, Mathematics - Optimization and Control, Connections (general theory), vakonomic dynamics
nonholonomic mechanics, Mathematics - Differential Geometry, connections, Sub-Riemannian geometry, sub-Riemannian geometry, Differential Geometry (math.DG), Optimization and Control (math.OC), 53C05, 53C17, 58E25, Applications of variational problems to control theory, FOS: Mathematics, Mathematics - Optimization and Control, Connections (general theory), vakonomic dynamics
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