Practical stability analysis for transient system dynamics

Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science

Volumn 222, Issue 11, 2008, Pages 2123-2135

  Meijaard, J P ^a,b   Popov, Atanas A ^a  

^a UNIVERSITY OF NOTTINGHAM   (United Kingdom)

^b UNIVERSITY OF TWENTE   (Netherlands)

Author keywords

Braking; Motorcycle dynamics; Multi body dynamics; Practical stability; Rotor dynamics; Stability criteria

Indexed keywords

AUTOMOBILE BODIES; AUTOMOBILE PARTS AND EQUIPMENT; DYNAMICS; EQUATIONS OF MOTION; MECHANICS; MOTORCYCLES; SYSTEM STABILITY;

BODY SYSTEMS; CALCULATION PROCEDURES; CRITICAL SPEEDS; FINITE TIMES; JEFFCOTT ROTORS; LYAPUNOV; MOTORCYCLE DYNAMICS; MULTI-BODY DYNAMICS; PRACTICAL STABILITY; PRACTICAL STABILITY ANALYSES; REAL SYSTEMS; REAR WHEELS; ROTOR DYNAMICS; TRANSIENT CONDITIONS; TRANSIENT SYSTEMS; WOBBLE MODES;

STABILITY CRITERIA;

EID: 57649139021     PISSN: 09544062     EISSN: None     Source Type: Journal    
DOI: 10.1243/09544062JMES889     Document Type: Article

References (35)

1. Lyapunov, A. M. The general problem of the stability of motion, 1992 (Taylor and Francis, London) [translation of the French translation from the Russian original published in Kharkov in 1892]; also published in Int. J. Control, 1992, 55, 531-773.
2. La Salle, J. and Lefschetz, S. Stability by Lyapunov's direct method, with applications, 1961 (Academic Press, New York).
3. Meijaard, J. P. and Popov, A. A. Stability analysis of braked vehicles with application to motorcycles. In Braking 2004, vehicle braking and chassis control (Eds D. Barton and A. Blackwood), 2004, pp. 15-24 (Professional Engineering Publishing, Bury St Edmunds and London).
4. Meijaard, J. P. and Popov, A. A. Practical stability analysis of multibody systems with application to the braking of a motorcycle. In Proceedings of the 5th Euromech Nonlinear Dynamics Conference (Eds D. H. van Campen, M. D. Lazurko, and W. P. J. M. van den Oever), 2005, pp. 541-548 (Eindhoven University of Technology Eindhoven).
5. Szebehely, V. Review of concepts of stability. Celest. Mech., 1984, 34, 49-64.
6. Malkin, J. G. Theorie der Stabilität einer Bewegung, 1959 (Akademie-Verlag, Berlin) [translated from the Russian edition, Moscow and Leningrad, 1952].
7. Guckenheimer, J. and Holmes, P. Nonlinear oscillations, dynamical systems, and bifurcations of vector fields, 1983 (Springer-Verlag, New York).
8. Thompson, J. M. T. and Stewart, H. B. Nonlinear dynamics and chaos, 2nd edition, 2002 (Wiley, Chichester), first edition published under the title Nonlinear dynamics and chaos, geometrical methods for engineers and scientists in 1986.
9. Hsu, C. S. Cell-to-cell mapping, a method of global analysis for nonlinear systems, 1987 (Springer-Verlag, New York).
10. Golub, G. H. and Van Loan, C. F. Matrix computations, 2nd edition, 1989 (The Johns Hopkins University Press, Baltimore, MD).
11. Sayers, M. W. Symbolic computer methods to automatically formulate vehicle simulation codes. Doctoral Dissertation, University of Michigan, Ann Arbor, MI, USA, 1990.
12. Sayers, M. W. Symbolic computer language for multibody systems. J. Guid. Control. Dyn., 1991, 14, 1153-1163.
13. Sayers, M. W. Symbolic vector/dyadic multibody formalism for tree-topology systems. J. Guid. Control. Dyn., 1991, 14, 1240-1250.
14. Anon. AutoSim™ reference manual 2.5±, 1997 (Mechanical Simulation Corporation, Ann Arbor, MI).
15. Anderson, E., Bai, Z., Bischof, C., Blackford, S., Demmel, J., Dongarra, J., Du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A., and Sorensen, D. LAPACK users' guide, 3rd edition, 1999 (SIAM, Philadelphia, PA).
16. MATLAB. The language of technical computing. The MathWorks, version 7, 2004.
17. Jeffcott, H. H. The lateral vibration of loaded shafts in the neighbourhood of a whirling speed - the effect of want of balance. Lond. Edin. Dublin Philos. Mag. J. Sci., 1919, 37(6), 304-314.
18. Meijaard, J. P. Applications of the singular value decomposition in dynamics. Comput. Methods Appl. Mech. Eng., 1993, 103, 161-173.
19. Sharp, R. S. The lateral dynamics of motorcycles and bicycles. Veh. Syst. Dyn., 1985, 14, 265-283.
20. Sharp, R. S. Stability, control and steering responses of motorcycles. Veh. Syst. Dyn., 2001, 35, 291-318.
21. Meijaard, J. P., Papadopoulos, J. M., Ruina, A., and Schwab, A. L. Linearized dynamics equations for the balance and steer of a bicycle: a benchmark and review. Proc. R. Soc. A, 2007, 463, 1955-1982.
22. Sharp, R. S. The stability and control of motorcycles. J. Mech. Eng. Sci., 1971, 13, 316-329.
23. Koenen, C. The dynamic behaviour of a motorcycle when running straight ahead and when cornering. Doctoral thesis, Delft University of Technology Delft, The Netherlands, 1983.
24. Sharp, R. S. and Limebeer, D. J. N. A motorcycle model for stability and control analysis. Multibody Syst. Dyn., 2001, 6, 123-142.
25. Cossalter, V. and Lot, R. A motorcycle multi-body model for real time simulations based on the natural coordinates approach. Veh. Syst. Dyn., 2002, 37, 423-447.
26. Sharp, R. S., Evangelou, S., and Limebeer D. J. N. Advances in the modelling of motorcycle dynamics. Multibody Syst. Dyn., 2004, 12, 251-283.
27. Bradley, J. and Wood, S. A. Some experiments on the factors affecting the motion of a four-wheeled vehicle when some of its wheels are locked. Proc. Instn Automob. Engrs, 1930/1, 25, 46-62.
28. Starks, H. J. H. and Lister, R. D. Experimental investigations on the braking performance of motor vehicles. Proc. Instn Mech. Engrs Automob. Div., 1954/5, 1954, 31-44, 49-56.
29. Koiter, W. T. Inleidende theoretische beschouwing over het slippen van motorvoertuigen bij geblokkeerde wielen. Unclassified report of the Laboratory of Engineering Mechanics, Delft University of Technology, Delft, The Netherlands, 1955.
30. Koiter, W. T. and Pacejka, H. B. Skidding of vehicles due to locked wheels. Proc. Instn Mech. Engrs, 1968/9, 183(3H), 3-18.
31. Sharp, R. S. The stability of motorcycles in acceleration and deceleration. In Braking of road vehicles (IMechE Conference Publications 1976-5), 1977, pp. 45-49 (Mechanical Engineering Publications, London).
32. Limebeer, D. J. N., Sharp, R. S., and Evangelou, S. The stability of motorcycles under acceleration and braking. Proc. Instn Mech. Engrs, Part C: J. Mechanical Engineering Science, 2001, 215, 1095-1109.
33. Meijaard, J. P. and Popov, A. A. Multi-body modelling and analysis into the non-linear behaviour of modern motor-cycles. Proc. IMechE, Part K: J. Multi-body Dynamics, 2007, 221, 63-76.
34. Meijaard, J. P. and Popov, A. A. Numerical continuation of solutions and bifurcation analysis in multibody systems applied to motorcycle dynamics. Nonlinear Dyn., 2006, 43, 97-116.
35. Sharp, R. S. and Giles, C. G. Motorcycle front wheel patter in heavy braking. In The dynamics of vehicles on roads and on tracks (Ed. J. K. Hedrick), 1984, pp. 578-590 (Swets and Zeitlinger, Lisse).