Numerical continuation of solutions and bifurcation analysis in multibody systems applied to motorcycle dynamics

Nonlinear Dynamics

Volumn 43, Issue 1-2, 2006, Pages 97-116

  Meijaard, J P ^a   Popov, A A ^a  

^a UNIVERSITY OF NOTTINGHAM   (United Kingdom)

Author keywords

Bifurcations; Continuation; Double pendulum; Motorcycle dynamics; Multibody dynamics

Indexed keywords

BIFURCATION (MATHEMATICS); COMPUTER SIMULATION; EQUATIONS OF MOTION; NONLINEAR SYSTEMS; PARAMETER ESTIMATION; PENDULUMS;

CONTINUATION; DOUBLE PENDULUM; MOTORCYCLE DYNAMICS; MULTIBODY DYNAMICS;

MOTORCYCLES;

EID: 31444450332     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-006-0753-y     Document Type: Conference Paper

References (39)

1. Schiehlen, W. (ed.), Multibody Systems Handbook, Springer-Verlag, Berlin, 1990.
2. Kortüm, W. and Sharp, R. S. (eds.), Multibody Computer Codes in Vehicle System Dynamics, Vehicle System Dynamics, Vol. 22(Suppl.), Swets and Zeitlinger, Lisse, The Netherlands, 1993.
3. Schiehlen, W., 'Multibody system dynamics, roots and perspectives', Multibody System Dynamics 1, 1997, 149-188.
4. Shabana, A. A., 'Flexible multibody dynamics, review of past and recent developments', Multibody System Dynamics 1, 1997, 189-222.
5. Allgower, E. L. and Georg, K., 'Numerical path following', in Handbook of Numerical Analysis, Vol. V: Techniques of Scientific Computing (Part 2), P. G. Ciarlet and J. L. Lions (eds.), Elsevier, Amsterdam, 1997, pp. 3-207.
6. Guckenheimer, J. and Holmes, P., Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag, New York, 1983.
7. Thompson, J. M. T. and Stewart, H. B., Nonlinear Dynamics and Chaos, Geometrical Methods for Engineers and Scientists, Wiley, Chichester, UK, 1986. [2nd edn., 2002]
8. Kuznetsov, Y. A., Elements of Applied Bifurcation Theory, 2nd edn., Springer-Verlag, New York, 1998. [1st edn., 1995]
9. Roth, B. and Freudenstein, F., 'Synthesis of path-generating mechanisms by numerical methods', ASME Journal of Engineering for Industry 85, 1963, 298-306.
10. Wampler, C. W., Morgan, A. P., and Sommese, A. J., 'Numerical continuation methods for solving polynomial systems arising in kinematics', ASME Journal of Mechanical Design 112, 1990, 59-68.
11. Crisfield, M. A., Non-Linear Finite Element Analysis of Solids and Structures, Vol. 1: Essentials, Wiley, Chichester, UK, 1991.
12. Wriggers, P. and Simo, J. C., 'A general procedure for the direct computation of turning and bifurcation points', International Journal for Numerical Methods in Engineering 30, 1990, 155-176.
13. Cardona, A. and Huespe, A., 'Continuation methods for tracing the equilibrium path in flexible mechanism analysis', Engineering Computations 15, 1998, 190-220.
14. Meijaard, J. P., 'Direct determination of periodic solutions of the dynamical equations of flexible mechanisms and manipulators', International Journal for Numerical Methods in Engineering 32, 1991, 1691-1710.
15. Meijaard, J. P., 'Direct determination of periodic solutions of mechanical dynamical systems', Archive of Applied Mechanics 64, 1994, 249-257.
16. Sayers, M. W., 'Symbolic Computer Methods to Automatically Formulate Vehicle Simulation Codes', Doctoral Dissertation, The University of Michigan, Ann Arbor, MI, 1990.
17. Sayers, M. W., 'Symbolic computer language for multibody systems', Journal of Guidance, Control, and Dynamics 14, 1991, 1153-1163.
18. Sayers, M. W., 'Symbolic vector/dyadic multibody formalism for tree-topology systems', Journal of Guidance, Control, and Dynamics 14, 1991, 1240-1250.
19. Anon., AutoSim™ Reference Manual Version 2.5+, Mechanical Simulation Corporation, Ann Arbor, MI, 1997.
20. Kane, T. R., Dynamics, Holt, Rinehart and Winston, New York, 1968.
21. Steele, G. L. Jr., Common Lisp, the Language, 2nd edn., Digital Press, USA, 1990.
22. Doedel, E., Keller, H. B., and Kernevez, J. P., 'Numerical analysis and control of bifurcation problems, (I) bifurcation in finite dimensions', International Journal of Bifurcation and Chaos 1, 1991, 493-520.
23. Doedel, E., Keller, H. B., and Kernevez, J. P., 'Numerical analysis and control of bifurcation problems, (II) bifurcation in infinite dimensions', International Journal of Bifurcation and Chaos 1, 1991, 745-772.
24. Doedel, E., Champneys, A. R., Fairgrieve, T. F., Kuznetsov, Y. A., Sandstede, B., and Wang, X. J., 'AUTO 97: Continuation and bifurcation software for ordinary differential equations', Technical Report, Department of Computer Science, Concordia University, Montreal, 1997.
25. Kane, T. R. and Levinson, D. A., 'A multibody motion stability analysis', Multibody System Dynamics 3, 1999, 287-299.
26. Sharp, R. S., 'The parametrically excited multi-pendulum', Multibody System Dynamics 5, 2001, 303-313, erratum, ibid. 6, 2001, 301-302.
27. Graham, D. and McRuer, D., 'Retrospective essay on nonlinearities in aircraft flight control', Journal of Guidance, Control, and Dynamics 14, 1991, 1089-1099.
28. Gantmacher, F., Lectures in Analytical Mechanics, Mir, Moscow, 1970.
29. Meijaard, J. P., 'Numerical continuation methods and bifurcation analysis applied to multibody system dynamics', in Proceedings of the ASME 2003 Design Engineering Technical Conferences and Computers and Information in Engineering Conference, A. A. Shabana (ed.), The American Society of Mechanical Engineers, New York, 2003, paper DETC2003/VIB-48310, Vol. 5A, pp. 63-70.
30. Sharp, R. S., 'A review of motorcycle steering behaviour and straight line stability characteristics', in Motorcycle Dynamics and Rider Control, SP-428, Society of Automotive Engineers, Warrendale, PA, 1978, paper 780303, pp. 1-6.
31. Sharp, R. S., 'The lateral dynamics of motorcycles and bicycles', Vehicle System Dynamics 14, 1985, 265-283.
32. Sharp, R. S., 'Stability, control, and steering responses of motorcycles', Vehicle System Dynamics 35, 2001, 291-318.
33. Sharp, R. S., 'The stability and control of motorcycles', Journal of Mechanical Engineering Science 13, 1971, 316-329.
34. Koenen, C., 'The Dynamic Behaviour of a Motorcycle When Running Straight Ahead and When Cornering', Doctoral Dissertation, Delft University Press, Delft, The Netherlands, 1983.
35. Sharp, R. S. and Limebeer, D. J. N., 'A motorcycle model for stability and control analysis', Multibody System Dynamics 6, 2001, 123-142.
36. Meijaard, J. P. and Popov, A. A., 'Application of non-linear dynamics to instability phenomena in motorcycles' [The Dynamics of Vehicles on Roads and on Tracks, M. Abe (ed.), Proceedings of the 18th IAVSD Symposium, Kanagawa, Japan, August 24-30, 2003], Vehicle System Dynamics 41(Suppl.), 2004, 567-576.
37. Struik, D. J., Lectures on Classical Differential Geometry, Addison-Wesley, Cambridge, MA, 1950.
38. Anon., Vehicle Dynamics Terminology, SAE J670e, Society of Automotive Engineers, Warrendale, PA, 1978.
39. Pacejka, H. B., Tyre and Vehicle Dynamics, Butterworth-Heinemann, Oxford, 2002.