On the theory of motion of nonholonomic systems. The reducing-multiplier theorem

This classical paper by S.A. Chaplygin presents a part of his research in non-holonomic mechanics. In this paper, Chaplygin suggests a general method for integration of the equations of motion for non-holonomic systems, which he himself called the “reducing-multiplier method”. The method is illustrated on two concrete problems from non-holonomic mechanics. This paper produced a considerable effect on the further development of the Russian non-holonomic community. With the help of Chaplygin’s reducing-multiplier theory the equations for quite a number of non-holonomic systems were solved (such systems are known as Chaplygin systems). First published about a hundred years ago, this work has not lost its scientific significance and is hoped to be estimated at its true worth by the English-speaking world.