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 nonholonomic 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 nonholonomic 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.
This publication contributes to the series of RCD translations of Chaplygin’s scientific heritage. In 2002 we published two of his works (both cited in this one) in the special issue dedicated to non-holonomic mechanics (RCD, Vol. 7, no. 2). These translations along with translations of his other two papers on hydrodynamics (RCD, Vol. 12, nos. 1,2) aroused considerable interest and are broadly cited by modern researches.