Reduced equations for nonholonomic mechanical systems with dissipative forces
type: Item
instance of: scholarly article
title: Reduced equations for nonholonomic mechanical systems with dissipative forces
zbMATH Open document ID: 0931.37021
DOI: 10.1016/S0034-4877(98)80010-4
author: Jim Ostrowski
published in: Reports on Mathematical Physics
publication date: 2000-03-07T00:00:00Z
review text: The main topic of the paper is the problem of computing reduced equation for mechanical systems both in the constrained (mixed kinematic and dynamic) and unconstrained case. In the latter one the structure of the reduced Lagrangian reveals the local forms of the locked inertia tensor and the mechanical connection, both useful components in the reduction process. This structure is surprisingly simple and can be deduced directly from the kinetic energy metric. For systems with nonholonomic constraints an extension to the known nonholonomic momentum equation that includes general forcing functions is given. The classical reduction, where invariants of the dynamics such as momenta of energy are factored out, is extended to include external nonholonomic constraints which are found mainly in robotic systems. So a wide range of applications in the field of mechanics and control of robotic and biological locomotion can be given, such as reorienting satellites with robotic arms, wheeled mobile robots and the snakeboard motions. The latter one is deeply investigated in an example discussion. In contrast to the prior work on this subject the author develops straightforward and efficient methods to generate the equations of motion in a structured or automated way. An overview of the Lagrangian formulation of nonholonomic reduction and matrix equations for the dynamics of systems with symmetries, external forces and constraints are provided. Extra attention is paid to the examination of Rayleigh dissipation functions to model viscous friction in locomotion systems.
Mathematics Subject Classification ID: 37J60
Mathematics Subject Classification ID: 70H33
Mathematics Subject Classification ID: 70F25
Mathematics Subject Classification ID: 70H03
Mathematics Subject Classification ID: 37J15
zbMATH DE Number: 1293240
zbMATH Keywords: Lie group symmetries
zbMATH Keywords: nonholonomic reduction
zbMATH Keywords: robotic locomotion
zbMATH Keywords: reduced Lagrangian
zbMATH Keywords: nonholonomic constraints
zbMATH Keywords: biological locomotion
zbMATH Keywords: Rayleigh dissipation
zbMATH Keywords: viscous friction
zbMATH Keywords: locomotion systems
describes a project that uses: Mathematica
describes a project that uses: Reduction.m
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1293240