Mechanical systems subjected to generalized non-holonomic constraints

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 457, Issue 2007, 2001, Pages 651-670

  Cortes J ^a   De Leon M ^a   De Diego, D Martín ^a,b   Martinez S ^a  

^a INSTITUTO DE MATEMÁTICAS Y FÍSICA FUNDAMENTAL   (Spain)

^b UNIVERSITY OF VALLADOLID   (Spain)

Author keywords

Impulsive forces; Mechanical systems; Non holonomic constraints

Indexed keywords

EID: 57249090235     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.2000.0686     Document Type: Article

References (32)

1. Appell, P. 1953 Traité de mécanique rationnelle, 6th edn, vol. 2. Paris: Gauthier-Villars.
2. Bates, L. & Śniatycki, J. 1992 Nonholonomic reduction. Rep. Math. Phys. 32, 99-115.
3. Bloch, A. M., Krishnaprasad, P. S., Marsden, J. E. & Murray, R. M. 1996 Nonholonomic mechanical systems with symmetry. Arch. Ration. Mech. Analysis 136, 21-99.
4. Brogliato, B. 1996 Nonsmooth impact mechanics: models, dynamics and control. Lectures Notes in Control and Information Science, no. 220. Springer.
5. Cantrijn, F., de León, M., Marrero, J. C. & Martín de Diego, D. 1998 Reduction of nonholonomic mechanical systems with symmetries. Rep. Math. Phys. 42, 25-45.
6. Chen, B., Wang, L. S., Chu, S. S. & Chou, W. T. 1997 A new classification of nonholonomic constraints. Proc. R. Soc. Lond. A 453, 631-642.
7. Cushman, R., Kemppainen, D., Śniatycki, J. & Bates, L. 1995 Geometry of nonholonomic constraints. Rep. Math. Phys. 36, 275-286.
8. de León, M. & Martín de Diego, D. 1996 On the geometry of non-holonomic Lagrangian systems. J. Math. Phys. 37, 3389-3414.
9. Ibort, A., de León, M., Lacomba, E. A., Martín de Diego, D. & Pitanga, P. 1997 Mechanical systems subjected to impulsive constraints. J. Phys. A 30, 5835-5854.
10. Ibort, A., de León, M., Lacomba, E. A., Marrero, J. C., Martín de Diego, D. & Pitanga, P. 1998 Geometric formulation of mechanical systems subjected to time-dependent one-sided constraints. J. Phys. A 31, 2655-2674.
11. Ibort, A., de León, M., Lacomba, E. A., Marrero, J. C., Martín de Diego, D. & Pitanga, P. 2000 Geometric formulation of Carnot's theorem. Preprint. IMAFF-CSIC.
12. Kane, T. R. 1968 Dynamics. New York: Holt, Rinehart and Winston.
13. Keller, J. B. 1986 Impact with friction. ASME J. Appl Mech. 53, 1-4.
14. Koiller, J. 1992 Reduction of some classical non-holonomic systems with symmetry. Arch. Ration. Mech. Analysis 118, 113-148.
15. Koon, W. S. & Marsden, J. E. 1997 The Hamiltonian and Lagrangian approaches to the dynamics of nonholonomic systems. Rep. Math. Phys. 40, 21-62.
16. Lacomba, E. A. & Tulczyjew, W. A. 1990 Geometric formulation of mechanical systems with one-sided constraints. J. Phys. A 23, 2801-2813.
17. Lewis, A. D. 1998 Affine connections and distributions with applications to nonholonomic mechanics. Rep. Math. Phys. 42, 135-164.
18. Marle, C. M. 1995 Reduction of constrained mechanical systems and stability of relative equilibria. Commun. Math. Phys. 174, 295-318.
19. Marle, C. M. 1998 Various approaches to conservative and nonconservative nonholonomic systems. Rep. Math. Phys. 42, 211-229.
20. Moreau, J. J. 1971 Mécanique classique, vol. 2. Paris: Masson.
21. Neimark, J. & Fufaev, N. 1972 Dynamics of nonholonomic systems. Transactions of Mathematical Monographs, vol. 33. American Mathematical Society.
22. Painlevé, P. 1930 Cours de mécanique, vol. 1. Paris: Gauthier-Villars.
23. Pugliese, F. & Vinogradov, A. M. 2000 Jumping oscillator. Preprint, math. DG/990215.
24. Rosenberg, R. 1977 Analytical dynamics. Plenum.
25. Stewart, D. E. 2000 Rigid-body dynamics with friction and impact. SIAM Rev. 42, 3-39.
26. Stronge, W. J. 1990 Rigid body collisions with friction. Proc. R. Soc. Lond. A 431, 169-181.
27. Stronge, W. J. 1991 Friction in collisions: resolution of a paradox. J. Appl. Phys. 69, 610-612.
28. Vaisman, I. 1994 Lectures on the geometry of Poisson manifolds. Progress in Mathematics, vol. 118. Basel: Birkhäuser.
29. van der Schaft, A. J. & Maschke, B. M. 1994 On the Hamiltonian formulation of nonholonomic mechanical systems. Rep. Math. Phys. 34, 225-233.
30. Vershik, A. M. 1984 Classical and non-classical dynamics with constraints. In Global analysis - studies and applications, vol. I. Springer Lecture Notes in Mathematics, no. 1108, pp. 278-301.
31. Vershik, A. M. & Faddeev, L. D. 1972 Differential geometry and Lagrangian mechanics with constraints. Sov. Phys. Dokl. 17, 34-36.
32. Vinogradov, A. M. & Kuperschmidt, B. A. 1977 The structures of Hamiltonian mechanics. Russ. Math. Surv. 32, 177-243.