The equation of motion for the system of the variable mass in the non-linear non-holonomic space
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The dot product of bases vectors on the super-surface of constraints of the non-linear non-holonomic space and Mesherskii equations may act as the equations of fundamental dynamics of mechanical system for the variable mass. These are very simple and convenient for computation. From these known equations, the equations of Chaplygin, Nielson, Appell, Mac-Millan et al., are derived; it is unnecessary to introduce the definition of Appell-Chetaev or Niu Qinping for the virtual displacement. These are compatible with the D'Alembert-Lagrange's principle.
Key wordsthe non-linear non-holonomic constraints the system of the variable mass dot product, bases vectors on supersurface of constraints Misherskii equation
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