On different forms of the theorem of kinetic energy


V. G. Rumyantsev




Different forms of the kinetic energy are considered for nonholonomic systems. Starting from the fact that the theorems on kinetic energy derived from the equations of Lagrange of the first and second kind are not equivalent in the case of finite rheonomous constraints, an expression for the determination of the power of the constraints reaction is derived in the form of the equations of Lagrange of the second kind for the variable $t=q_0$. The system of equations for $q_i$, $q_0$ allows the formulation of a general theorem on kinetic energy in a deferential or in a finite form.