BIFURCATIONS OF STEADY STATES OF THE BIAXIAL CREW MODEL

Abstract

Many transport systems (car, airplane, ship) have symmetry property. For such systems symmetrical deviations of some control parameter (steering wheel) from the neutral position lead to symmetry of the dynamic behaviour of the object (equivalence of left and right turns). In this case the straight-line motion of an object with constant velocity corresponds to a trivial solution of the corresponding dynamic system (symmetric solution). Conditions for dangerous-safe loss of symmetric junction stability (the case of one zero proper linear approximation system) can be obtained from the analysis of the true birth-fusion of stationary states with a stationary state corresponding to a symmetric solution. This approach makes it possible to obtain conditions of dangerous and safe loss of symmetric junction stability equivalent to the conditions of MM. Bautin [3] with the lowest possible computational cost. The proposed approach is illustrated by the example of the stability analysis of a nonlinear model of a double-axle crew with excessive rotation. It is shown that the condition of hazardous and safe loss of stability of straight-line motion (symmetric junction) is determined by the ratio between dimensionless coefficients of axle deflection and coupling coefficients on transaxle axes. However, clutch coefficients are not included in the linear system of equations of perturbed motion but refer to a substantially nonlinear characteristic of the forces of withdrawal.