Abstract
Nonholonomic systems provide an important class of mechanical control systems. One reason for this importance is that nonintegrability is essential to both the mechanics and the control: Nonintegrable constraint distributions are the essence of nonholonomic systems, while a nonintegrable distribution of control vector fields is the key to controllability of nonlinear systems. We will learn how these two different types of nonintegrability work together when we study control of nonholonomic mechanical systems.
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References
This example is also treated in Appel [1900] and Korteweg [1899]. For this example from a more modern point of view, see, for example, O’Reilly [1996], and Getz and Marsden [1994].
This is proved by a nice technique of Birkhoff utilizing the reversible symmetry in Hermans [1995].
We will see how to view A(q) intrinsically in the next section. Here, we do not consider nonholonomic constraints which are nonlinear in the velocities. Discussion of such constraints may be found, for example, in Appell [1911], Marie [1996, 1998], and Terra and Kobayashi [2002] and references therein.
This would take us into the subject of singular nonholonomic reduction; see, for example, Bates [1998].
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© 2003 Springer-Verlag New York, Inc.
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Bloch, A.M. (2003). Nonholonomic Mechanics. In: Nonholonomic Mechanics and Control. Interdisciplinary Applied Mathematics, vol 24. Springer, New York, NY. https://doi.org/10.1007/b97376_5
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DOI: https://doi.org/10.1007/b97376_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3043-9
Online ISBN: 978-0-387-21644-7
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