Analysis of divergent bifurcations in the dynamics of wheeled vehicles
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Published:2022-04-04
Issue:1
Volume:13
Page:321-329
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ISSN:2191-916X
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Container-title:Mechanical Sciences
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language:en
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Short-container-title:Mech. Sci.
Author:
Verbitskii Vladimir, Lobas Vlad, Misko YevgenORCID, Bondarenko Andrey
Abstract
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.
Publisher
Copernicus GmbH
Subject
Industrial and Manufacturing Engineering,Fluid Flow and Transfer Processes,Mechanical Engineering,Mechanics of Materials,Civil and Structural Engineering,Control and Systems Engineering
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