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

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.