| Abstract: | This work analyzes energy relations between nonholonomic systems, whose motion is restricted by nonholonomic constraints of arbitrary form and origin. Such constraints can be natural, originating from spontaneous formulation of the problem, or artificial, expressing some program motion in control theory. On the basis of corresponding Lagrange’s equations, a general law of the change in energy d?/dt was formulated for such systems by the help of which it has been shown that here there exist two types of laws of conservation of energy, depending on the structure of work of these reaction forces. Also, the condition for existence of this second type of the law of conservation of energy has been formulated in the form of the system of differential equations. The results obtained are illustrated by a number of examples, with natural nonlinear constraints, as well as with artificial ones that express some program motion. |
