The Hamiltonian and Lagrangian approaches to the dynamics of nonholonomic systems

Abraham, 1978 V. I. Arnold: Dynamical Systems III. Encyclopedia of Mathematics 3, Springer, Berlin. Bates, 1996, Rep. Math. Phys., 37, 295, 10.1016/0034-4877(96)84069-9 Bates, 1993, Rep. Math. Phys., 32, 99, 10.1016/0034-4877(93)90073-N Bloch, 1992, On the dynamics and control of nonholonomic systems on Riemannian manifolds, 368 Bloch, 1994, SIAM J. Control Optim. Bloch, 1994, 33, 2584 A. M. Bloch and P. Crouch: Reduction of Euler Lagrange problems for constrained variational problems and relation with optimal control problems. 33rd CDC, to appear. Bloch, 1996, Arch. Ration. Mech. Annal., 136, 21, 10.1007/BF02199365 Cushman, 1995, The rolling disc, 19 Dazord, 1994, Illinois J. Math., 38, 148, 10.1215/ijm/1255986892 Getz, 1994, Control of balance for a nonlinear nonholonomic non-minimum phase model of a bicycle Getz, 1995, Control for an autonomous bicycle Getz, 1996, Dynamic Inversion of Nonlinear Maps with Applications to Nonlinear Control and Robotics Hermans, 1995, Nonlinearity, 8, 493, 10.1088/0951-7715/8/4/003 Koiller, 1992, Arch. Rat. Mech. Anal., 118, 113, 10.1007/BF00375092 Koon, 1997, Reduction, Reconstruction and Optimal Control for Nonholonomic Mechanical Systems with Symmetry Koon, 1997, SIAM J. Control Optim., 35, 901, 10.1137/S0363012995290367 Krishnaprasad, 1992 A. Lewis: Affine connections and distributions, preprint. Marle, 1995, Commun. Math. Phys., 174, 295, 10.1007/BF02099604 Marsden, 1992, Lectures on Mechanics, 174 Marsden, 1990, Reduction, Symmetry, and Phases in Mechanics, Memoirs AMS, 436 Marsden, 1992, An Introduction to Mechanics and Symmetry, 17 Marsden, 1993, Z Angew. Math. Phys., 44, 17, 10.1007/BF00914351 Marsden, 1993, Fields Institute Commun., 1, 139 Ostrowski, 1996, The Mechanics and Control of Undulatory Robotic Locomotion J. Ostrowski, J. P. Desai and V. Kumar: Optimal gait selection for nonholonomic locomotion systems, Proc. CDC, to appear. van der Schaft, 1994, Rep. Math. Phys., 34, 225, 10.1016/0034-4877(94)90038-8 Vershik, 1994, Nonholonomic dynamical systems, geometry of distributions and variational problems, 1 Weber, 1986, Arch. Ration. Mech. Anal., 91, 309, 10.1007/BF00282337 Yang, 1993, Chaplygin dynamics and Lagrangian reduction