Nonholonomic Control Systems on Riemannian Manifolds
- 1 January 1995
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Control and Optimization
- Vol. 33 (1) , 126-148
- https://doi.org/10.1137/s036301299223533x
Abstract
This paper gives a general formulation of the theory of nonholonomic control systems on a Riemannian manifold modeled by second-order differential equations and using the unique Riemannian connection defined by the metric. The main concern is to introduce a reduction scheme, replacing some of the second-order equations by first-order equations. The authors show how constants of motion together with the nonholonomic constraints may be combined to yield such a reduction. The theory is applied to a particular class of nonholonomic control systems that may be thought of as modeling a generalized rolling ball. This class reduces to the classical example of a ball rolling without slipping on a horizontal plane.Keywords
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