Numerical Continuation of Solutions and Bifurcation Analysis in Multibody Systems Applied to Motorcycle Dynamics

It is shown how the equations of motion for a multibody system can be generated in a symbolic form and the resulting equations can be used in a program for the analysis of nonlinear dynamical systems. Stationary and periodic solutions are continued when a parameter is allowed to vary and bifurcation...

Full description

Saved in:
Bibliographic Details
Published in:Nonlinear dynamics 2006-01, Vol.43 (1-2), p.97-116
Main Authors: Meijaard, J P, Popov, A A
Format: Article
Language:English
Subjects:
Bifurcations
Cornering
Equations of motion
Hopf bifurcation
Motorcycles
Multibody systems
Nonlinear analysis
Nonlinear systems
Parameters
Pendulums
Viability
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:It is shown how the equations of motion for a multibody system can be generated in a symbolic form and the resulting equations can be used in a program for the analysis of nonlinear dynamical systems. Stationary and periodic solutions are continued when a parameter is allowed to vary and bifurcations are found. The variational or linearized equations and derivatives with respect to parameters are also provided to the analysis program, which enhances the efficiency and accuracy of the calculations.The analysis procedure is firstly applied to a rotating orthogonal double pendulum, which serves as a test for the correctness of the implementation and the viability of the approach. Then, the procedure is used for the analysis of the dynamics of a motorcycle. For running straight ahead, the nominal solution undergoes Hopf bifurcations if the forward velocity is varied, which lead to periodic wobble and weave motions. For stationary cornering, wobble instabilities are found at much lower speeds, while the maximal speed is limited by the saturation of the tyre forces.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-006-0753-y