Complete identification of chaos of nonlinear nonholonomic systems

The chaos of nonholonomic systems with two external nonlinear nonholonomic constraints where the magnitude of velocity is a constant and the magnitude of the velocity is a constant with a periodic disturbance, respectively, is completely identified for the first time. The scope of the chaos study is extended to nonlinear nonholonomic systems. By applying the nonlinear nonholonomic form of Lagrange’s equations, the dynamic equation is expressed. The existence of chaos in these two nonlinear nonholonomic systems is first wholly proved by all numerical criteria of chaos, i.e., the most reliable Lyapunov exponents, phase portraits, Poincaré maps, and bifurcation diagrams. Furthermore, it is found that the Feigenbaum number still holds for nonlinear nonholonomic systems.