INTEGRATION METHOD FOR THE DYNAMICS EQUATION OF RELATIVE MOTION OF VARIABLE MASS NONLINEAR NONHOLONOMIC SYSTEM

1.IntroductionMoreandmoreattentionhasbeenpaidtothestudyofdynamicsofcomplicatedsystemwiththedevelopmentofmodernscienceandtechnology.Thestudyoftherelativemotionofvariablemasssystembyusingthetheoryandmethodofanalyticalmechanicsnotonlycanunifytheexpressionformbutalsocandisplayitssuperioritytothecomplicatedsystem.In1961,thedynamicsofrelativemotionofholonomicsystemwasderivedbyLur'ell].Inrecehtyears,LiulZIandLuol3'4]havegiventhedynamicsequationsofrelativemotionofvariablemassnonholonomicsystem.Howe…

Integration method for the dynamics equation of relative motion of variable mass nonlinear nonholonomic system

In this paper, the integration methods of dynamics equations of relative motion of variable mass nonlinear nonholonomic system are given such as the gradient method,the single-component method and thefield method. Firstly, the dynamics equations arewritten in the canonical form and the field form. Secondly, the gradient method, thesingle-component method and the field method are used to integrate the dynamicsequations of the corresponding constant mass holonomic system in inerial referenceframe respectively. With the restriction of nonholonomic constraints to the initialconditions being considered, the solutions of the dynamics equations of variable massnonlinear nonholonomic system in noninertial reference frame are obtained.