Bifurcation sets and catastrophes in manifolds of steady states of pneumatic-tired machines under constant mechanical loads

Journal Article · Fri Sep 01 04:00:00 EDT 1995 · International Applied Mechanics

DOI:https://doi.org/10.1007/BF00846902· OSTI ID:186165

Verbitskii, V G ^[1]

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1. S.P. Timoshenko Institute of Mechanics, Kiev (Ukraine)

In this article, we examine the steady motions of pneumatic-wheeled machines within the framework of the phenomenological approach developed by I. Rokar. The manipulated variables are longitudinal velocity v, the angle {theta} of rotation of the front wheels relative to the body of the machine, the lateral force Q applied at the center of mass C, and the moment of the forces M relative to the vertical axis. A procedure is proposed for constructing a bifurcation surface in explicit or parametric form without constructing the set of steady states. At Q = O and M = O, the bifurcation curve has a cusp. Such a cusp is characteristic of the catastrophe set. The introduction of the third parameter Q does not change the character of the bifurcation set, but it does shift its boundaries and, in so doing, lowers the critical linear velocity. The parameter M is important from the viewpoint of catastrophe theory, since it changes the dimensionality fo the catastrophe space. A `dovetail` singularity is realized when M = 0.

• Sponsoring Organization: USDOE
• OSTI ID: 186165
• Journal Information: International Applied Mechanics, Journal Name: International Applied Mechanics Journal Issue: 3 Vol. 31; ISSN IAMEEU; ISSN 1063-7095
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
99 GENERAL AND MISCELLANEOUS
BIFURCATION
DIFFERENTIAL EQUATIONS
EQUATIONS OF MOTION
MACHINERY
NONLINEAR PROBLEMS
WHEELS