EQUATIONS OF MOTION OF VARIABLE MASS NONHOLONOMIC DYNAMICAL SYSTEMS IN POINCARé-CHETAEV VARIABLES

The equations of motion of variable-mass nonlinear nonholonomic dynamical systems in Poincaré-Chetaev variables have been studied. Firstly, the Poincaré-Chetaev variables x1,x2,…,xn and more with n-m holonomic constraints and m-l nonlinear nonholonomic constraints of Chetaev type were introduced. Secondly, the equations of Chaplygin's form, Nielsen's form and Appell's form were derived from the D'Alembert-Lagrange principle for a variable-mass mechanical system. Finally, the problem of equivalence between the Chaplygin's equations and the Appell's equations was discussed. Then the theory is illustrated by an example due to Appell.