ON ROUTH REDUCTION AND ITS APPLICATION IN RIGID-BODY DYNAMICS

Routh reduction is a standard process reducing the system of Lagrange equations in generalized coordinates to a lower dimension system by us e of first integrals corresponding to cyclic coordinates (see [1, 2]). Here we demonstrate how this reduction can be performed for the Lagra nge-Poincare' system describing the motion of a rigid body about a fix ed point written with dependent coordinates and nonholonomic velocitie s. Some examples from a rigid body dynamics are considered. The idea o f this method arises to the paper of LYAPUNOV [3]. The theory of the R outh reduction Sor the systems described by equations involving non-ho lonomic coordinates was developed in [4, 5]. The development of the ap proach of LYAPUNOV was done in [6].