Integral theory for the dynamics of nonlinear nonholonomic system in noninertial reference frames

This paper establishes the integral theory for the dynamics of nonlinear nonholonomic system in noninertial reference frame. Firstly, based on the Routh equation of the relative motion of nonlinear nonholonomic system gives the first integral of the system. Secondly, by using cyclic integral or energy integral reduces the order of the equation and obtains generalized Routh equation and Whittaker equation respectively. Thirdly, derives canonical equation and variation equation and by using the first integral constructs integral invariant. And then, establishes the basic integral variants and the integral invariant of Poincare-Cartan type. Finally, we give a series of deductions.