Nonholonomic multibody dynamics

Multibody System Dynamics

Volumn 9, Issue 3, 2003, Pages 213-236

  Kielau, Gerald ^a   Maißer, Peter ^a  

^a CHEMNITZ UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Lagrangian equations; Nonholonomic multibody systems; Riemannian geometry

Indexed keywords

COMPUTATIONAL GEOMETRY; COMPUTER SIMULATION; CONSTRAINT THEORY; EQUATIONS OF MOTION; KINEMATICS; LAGRANGE MULTIPLIERS; MATHEMATICAL MODELS; NONLINEAR CONTROL SYSTEMS;

LAGRANGIAN EQUATIONS; NONHOLONOMIC MULTIBODY SYSTEMS; RIEMANNIAN GEOMETRY;

DYNAMICS;

EID: 0038681969     PISSN: 13845640     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022920709192     Document Type: Article

References (41)

1. Arnold, V.J., Mathematical Methods of Classical Mechanics, Springer-Verlag, Berlin, 1989.
2. Blajer, W., 'Dynamic analysis of constrained multibody systems in orthonormalized tangent space', in Advanced Multibody System Dynamics, W. Schiehlen (ed.), Kluwer Academic Publishers, Dordrecht, 1993, 415-420.
3. Bloch, A.M., Krishnaprasad, P.S., Marsden, J.E. and Murray, R.M., 'Nonholonomic mechanical systems with symmetry', CDS Technical Report 94-013, California Institute of Technology 1995.
4. Brockett, R.W., 'Control theory and singular Riemannian geometry', in New Directions in Applied Mathematics, P. Huston and G. Young (eds), Springer-Verlag, New York, 1981, 11-27.
5. Bullo, F. and Žefran, M., 'On mechanical control systems with nonholonomic constraints and symmetries', Systems & Control Lett. 45, 2002, 133-143.
6. Caratheodory, C., 'Der Schlitten', ZAMM 13(2), 1933, 71-76.
7. Enos, M.J. (ed.), Dynamics and Control of Mechanical Systems, Fields Institute Communications, American Mathematical Society, Providence, RI, Vol. 1, 1993.
8. Enos, M.J., 'On an optimal control problem on SO(3) × SO(3) and the falling cat', in Dynamics and Control of Mechanical Systems. Fields Institute Communications, M.J. Enos (ed.), American Mathematical Society, Providence, MI, 1993, 75-112.
9. Hamel, G., 'Über nichtholonome Systeme', Math. Annalen 92, 1924, 33-41.
10. Jacubczyk, B. and Respondek, W., 'On linearization of control systems', Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 28, 1980, 517-522.
11. Kane, T. R., 'Dynamics of nonholonomic systems', J. Appl. Mech. 28, 1961, 574-578.
12. Kane, T.R. and Scher, M.P., 'A dynamical explanation of the falling cat phenomenon', Internat. J. Solids and Structures 5, 1969, 663-670.
13. Kane, T.R., 'Nonholonomic multibody systems containing gyrostats', in Dynamics of Multibodysystems, IUTAM Symposium, München, K. Magnus (ed.), Springer-Verlag, Berlin, 1978, 97-107.
14. Kron, G., 'Non Riemannian dynamics of rotating electrical machinery', J. Math. Phys. 13, 1934, 103-194.
15. Laumond, J.-P., 'Finding collision-free smooth trajectories for a nonholonomic mobile robot', in International Joint Conference on Artificial Intelligence, J. McDermott (ed.), Morgan Kaufmann, San Mateo, CA, 1987, 1120-1123.
16. Lovelock, D. and Rund, H., Tensors, Differential Forms, and Variational Principles. Dover Publication, New York, 1975.
17. Maisser, P., 'Modellgleichungen für Manipulatoren', Techn. Mech. 3(2), 1982, 64-78.
18. Maisser, P., 'Ein Beitrag zur Theorie diskreter elektromechanischer Systeme mit Anwendungen in der Manipulator-/Robotertechnik', Dissertation B, TH Ilmenau, 1984.
19. Maisser, P., 'Analytische Dynamik von Mehrkörpersystemen', ZAMM 68(10), 1988, 463-481.
20. Maisser, P., 'Theoretische Untersuchungen zum Fahrverhalten von Bobschlitten', Forschungsbericht, Institut für Mechanik, Karl-Marx-Stadt, 1989.
21. Maisser, P., 'A differential geometric approach to the multi body system dynamics', ZAMM 71(4), 1991, T116-T119.
22. Maisser, P., 'Differential-geometric methods in multibody dynamics', Nonlinear Anal. Theory Methods Appl. 30(8), 1997, 5127-5133.
23. Maisser, P., 'Brachystochronen als zeitkürzeste Fahrspuren von Bobschlitten', ZAMM 78(5), 1998, 311-319.
24. Maisser, P. and Jungnickel, U., 'Lyapunov-stable position control of constrained multibody systems', in Proceedings 3rd International Heinz Nixdorf Symposium on Mechatronics and Advanced Motion Control, Uni-GH Paderborn, Germany, May 27-28, J. Wallaschek, J. Lückel and W. Littmann (eds.), Heinz Nixdorf Institut, 1999, 61-66.
25. Maisser, P. and Jungnickel, U., 'Stability of controlled motion of a gymnast in high-speed mid air maneuvers', in Proceedings IUTAM Symposium on Recent Developments in Nonlinear Oscillations of Mechanical Systems, Hanoi, Vietnam, March 2-5, 1999, N.V. Dao and E.J. Kreuzer (eds.), Kluwer Academic Publishers, Dordrecht, 2000, 121-130.
26. Marsden, J.E. and Ratiu, T.S., Introduction to Mechanics and Symmetry, Springer-Verlag, New York, 1994.
27. Maschke, B.M. and Van der Schaft, A.J., 'A Hamiltonian approach to stabilization of non-holonomic mechanical systems', in Proceedings 33rd IEEE CDC, Orlando, FL, U.S.A., 1994, 2950-2954.
28. Modi, V.J., 'On the dynamics and Control of the evolving space station 'Freedom'', in Dynamics and Control of Machanical Systems. Fields Institute Communications, M.J. Enos (ed.), American Mathematical Society, Providence, RI, 1993, 165-192.
29. Murray, R.M., Zexiang Li and Sastry, S.S., A Mathematical Introduction to Robotic Manipulation, CRC Press, Boca Raton, FL, 1994.
30. Nejmark, J.I. and Fufaev, N.A., Dinamika negolonomnych sistem, Isdvo 'Nauka', Moscow, 1967 [in Russian].
31. Nijmeijer, H. and van der Schaft, A., Nonlinear Dynamical Control Systems, Springer-Verlag, Berlin, 1996.
32. Ostrowski, J., Lewis, A., Murray, R.M. and Burdick, J., 'Nonholonomic mechanics and locomotion: the snakeboard example', in IEEE International Conference on Robotics and Automation, E. Straub and R.S. Sipple (ed.), IEEE, New York, 1994, 2391-2397.
33. Papastavridis, J.G., Tensor Calculus and Analytical Dynamics, CRC Press, Boca Raton, FL, 1999.
34. Pfeiffer, F. and Glocker, Ch., Multibody Dynamics with Unilateral Constraints, John Wiley & Sons, New York, 1996.
35. Pfeiffer, F., 'Robots with unilateral constraints', Ann. Rev. Control 22, 1998, 121-132.
36. Renger, A., 'Theorie der Bewegung eines Radsatzes auf geradem Gleis mit stochastischen Gleislagefehlern', ZAMM 62(3), 1998, 141-169.
37. Steigenberger, J., 'On a class of nonlinear control systems which are feedback equivalent to systems affine in the control', in Proceedings der internationalen Tagung mathematische Optimierung - Theorie und Anwendungen, Eisenach, Germany, 10-15 November, TU Ilmenau, 1986, 143-144.
38. Steigenberger, J., 'Classical framework for nonholonomic mechanical control systems', Internat. J. Robust Nonlinear Control 5, 1995, 331-342.
39. Steigenberger, J., 'On nonholonomic systems and biomorphic motion', in Proceedings 44th International Scientific Colloquium, Technical University of Ilmenau, September 20-23, W. Gens (ed.), Vortragsreihe Bd. 2, 1999, 216-219.
40. Tseng, F.C. and Hulbert, G.M., 'Network-distributed multibody dynamics simulation - Gluing algorithm', in Advances in Computational Multibody Dynamics, J.A.C. Ambrósio and W.O. Schiehlen (eds.), IDMEC/IST, Lisbon, Portugal, 1999, 521-540.
41. Zhang, Y.L., Hubbard, M. and Huffman, R.K., 'Optimum control of bobsled steering', JOTA 85(1), 1995, 1-19.