Towards a Hamilton–Jacobi theory for nonholonomic mechanical systems

In this paper, we obtain a Hamilton–Jacobi theory for nonholonomic mechanical systems. The results are applied to a large class of nonholonomic mechanical systems, the so-called Caplygin systems.

[1]  E. Hairer,et al.  Geometric Numerical Integration: Structure Preserving Algorithms for Ordinary Differential Equations , 2004 .

[2]  The generalized Hamilton-Jacobi method for nonholonomic dynamical systems of Chetaev's type , 1975 .

[3]  M. Pavon.  Generalized Hamilton-Jacobi equations for nonholonomic dynamics , 2004, math-ph/0406008.

[4]  V. Arnold.  Mathematical Methods of Classical Mechanics , 1974 .

[5]  Frans Cantrijn,et al.  On almost-Poisson structures in nonholonomic mechanics , 1999 .

[6]  Second form of the generalized Hamilton-Jacobi method for nonholonomic dynamical systems , 1978 .

[7]  Jerrold E. Marsden,et al.  Foundations of Mechanics: 2nd Edition , 1980 .

[8]  R. Eden.  The Hamiltonian dynamics of non-holonomic systems , 1951, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[9]  Forms of Hamilton's principle for nonholonomic systems , 2000 .

[10]  Motion of a rolling disk by a new generalized Hamilton-Jacobi method , 1976 .

[11]  A universal Hamilton-Jacobi equation for second-order ODEs , 1999 .

[12]  D. D. Diego,et al.  Solving non-holonomic Lagrangian dymanics in terms of almost product structures , 1996 .

[13]  C. Godbillon.  Géométrie différentielle et mécanique analytique , 1969 .

[14]  L. Bates,et al.  What is a completely integrable nonholonomic dynamical system , 1999 .

[15]  M. de Leon,et al.  Geometric integrators and nonholonomic mechanics , 2002 .

[16]  P. Krishnaprasad,et al.  Nonholonomic mechanical systems with symmetry , 1996 .

[17]  A. Bloch,et al.  Nonholonomic Mechanics and Control , 2004, IEEE Transactions on Automatic Control.

[18]  R. Bains,et al.  Methods of differential geometry in analytical mechanics , 1992 .

[19]  David Martín de Diego,et al.  On the geometry of non‐holonomic Lagrangian systems , 1996 .

[20]  Reduction of constrained systems with symmetries , 1999 .

[21]  Geometric Hamilton-Jacobi theory , 2006, math-ph/0604063.

[22]  Larry Bates,et al.  Examples of gauge conservation laws in nonholonomic systems , 1996 .

[23]  F. Pirani.  MATHEMATICAL METHODS OF CLASSICAL MECHANICS (Graduate Texts in Mathematics, 60) , 1982 .

[24]  P J Fox,et al.  THE FOUNDATIONS OF MECHANICS. , 1918, Science.

[25]  V. Kozlov.  On the Integration Theory of Equations of Nonholonomic Mechanics , 2005, nlin/0503027.

[26]  J. Cortes,et al.  On the geometry of generalized Chaplygin systems , 2002, Mathematical Proceedings of the Cambridge Philosophical Society.