Abstract
Routh reduction is a standard process reducing the system of Lagrange equations in generalized coordinates to a lower dimension system by use of first integrals corresponding to cyclic coordinates (see [1, 2]). Here we demonstrate how this reduction can be performed for the Lagrange-Poincaré system describing the motion of a rigid body about a fixed point written with dependent coordinates and nonholonomic velocities. Some examples from a rigid body dynamics are considered. The idea of this method arises to the paper of Lyapunov [3]. The theory of the Routh reduction for the systems described by equations involving non-holonomic coordinates was developed in [4, 5]. The development of the approach of Lyapunov was done in [6].
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