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On Routh Reduction and its Application in Rigid Body Dynamics
Author(s) -
Bourov A.,
Chevallier D.
Publication year - 1998
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/(sici)1521-4001(199810)78:10<695::aid-zamm695>3.0.co;2-x
Subject(s) - generalized coordinates , nonholonomic system , mathematics , reduction (mathematics) , rigid body , holonomic , lyapunov function , rigid body dynamics , holonomic constraints , dimension (graph theory) , lyapunov stability , classical mechanics , control theory (sociology) , mathematical analysis , physics , computer science , nonlinear system , geometry , control (management) , pure mathematics , quantum mechanics , artificial intelligence , robot , mobile robot
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].