Routh's method for the nonholonomic systems (Q1123661)

In analytical mechanics, consider a conservative holonomic system which can be described by the standard form of Lagrange's equations, that is (*)(d/dt)(\(\partial L/\partial \dot q_ i)-(\partial L/\partial q_ i)=0\) \((i=1,2,...,n)\). It may happen that some of the coordinates are cyclic. Corresponding to each cyclic coordinate, there is a first integral of the system, which is called cyclic integral. By constructing the Routhian function, the cyclic integrals can be utilised to reduce the order of the set of Lagrangian differential equations of motion having the same form as Eq.(*). This is the famous Routh's method in analytical mechanics. In this note the Routhian function is generalized to the nonholonomic systems and the problem of using cyclic integrals of the nonholonomic systems to reduce the order of Chaplygin's equations of the nonholonomic systems under certain conditions is studied.