Back to Search
Start Over
Analysis of divergent bifurcations in the dynamics of wheeled vehicles
- Source :
- Mechanical Sciences. 13:321-329
- Publication Year :
- 2022
- Publisher :
- Copernicus GmbH, 2022.
-
Abstract
- This paper presents the bifurcation approach to analyze divergent loss of stability of the symmetric solution of a nonlinear dynamic model in Lyapunov's critical case of a single zero root. Under such a condition, material birth-annihilation bifurcations of multiple stationary states take place. Moreover, the equilibrium surface of stationary states in a small neighborhood of the symmetric solution is a generalized Whitney fold. In the simplest case of a fold peculiarity, the corresponding bifurcation manifold locally coincides with the discriminant manifold of a third-degree polynomial that determines the manifold of stationary states in a small neighborhood of the symmetric solution. An algorithm to construct the corresponding polynomial is introduced. Through the algorithm, the bifurcation manifold is determined, and the conditions for safe/unsafe loss of stability of the symmetric solution are derived analytically. The proposed approach to analyze divergent loss of stability is implemented for a nonlinear bicycle model of a two-axle wheeled vehicle. It represents a further development of Pevzner–Pacejka's well-known graph-analytical method. The paper determines the critical values of constructive parameters that are responsible for safe/unsafe loss of stability of the vehicle's straight-line motion, and it discusses strategies for the bifurcation approach to analyze divergent loss of stability.
Details
- ISSN :
- 2191916X
- Volume :
- 13
- Database :
- OpenAIRE
- Journal :
- Mechanical Sciences
- Accession number :
- edsair.doi...........614d6be88f3cb85fceb469f3b4b723a9