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On the equations of motion in constrained multibody dynamics

Lidström, Per LU (2012) In Mathematics and Mechanics of Solids 17(3). p.209-242
Abstract
The equations of motion for a constrained multibody system are derived from a continuum mechanical point of view. This will allow for the presence of rigid, as well as deformable, parts in the multibody system together with kinematical constraints. The approach leads to the classical Lagrange-d'Alembert equations of motion under constraint conditions. The generalized forces appearing in the equations of motion are given as expressions involving contact, internal and body forces in the sense of continuum mechanics. A detailed analysis of physical constraint conditions and their implication for the equations of motion is presented. A precise distinction is made between constraints on the motion on the one hand and resistance to the motion on... (More)
The equations of motion for a constrained multibody system are derived from a continuum mechanical point of view. This will allow for the presence of rigid, as well as deformable, parts in the multibody system together with kinematical constraints. The approach leads to the classical Lagrange-d'Alembert equations of motion under constraint conditions. The generalized forces appearing in the equations of motion are given as expressions involving contact, internal and body forces in the sense of continuum mechanics. A detailed analysis of physical constraint conditions and their implication for the equations of motion is presented. A precise distinction is made between constraints on the motion on the one hand and resistance to the motion on the other. Transformation properties - covariance and invariance under changes of configuration coordinates - are elucidated. The elimination and calculation of the so-called Lagrangian multipliers is discussed and some useful reformulations of the equations of motion are presented. Finally a Power theorem for the constrained multibody system is proved. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
constraints, equations of motion, multibody dynamics
in
Mathematics and Mechanics of Solids
volume
17
issue
3
pages
209 - 242
publisher
SAGE Publications Inc.
external identifiers
  • wos:000303650900001
  • scopus:84860737849
ISSN
1741-3028
DOI
10.1177/1081286511407111
language
English
LU publication?
yes
id
868e5299-a77a-4a41-b83d-9779840f7ab1 (old id 2551734)
date added to LUP
2012-05-31 09:22:15
date last changed
2017-08-20 03:18:42
@article{868e5299-a77a-4a41-b83d-9779840f7ab1,
  abstract     = {The equations of motion for a constrained multibody system are derived from a continuum mechanical point of view. This will allow for the presence of rigid, as well as deformable, parts in the multibody system together with kinematical constraints. The approach leads to the classical Lagrange-d'Alembert equations of motion under constraint conditions. The generalized forces appearing in the equations of motion are given as expressions involving contact, internal and body forces in the sense of continuum mechanics. A detailed analysis of physical constraint conditions and their implication for the equations of motion is presented. A precise distinction is made between constraints on the motion on the one hand and resistance to the motion on the other. Transformation properties - covariance and invariance under changes of configuration coordinates - are elucidated. The elimination and calculation of the so-called Lagrangian multipliers is discussed and some useful reformulations of the equations of motion are presented. Finally a Power theorem for the constrained multibody system is proved.},
  author       = {Lidström, Per},
  issn         = {1741-3028},
  keyword      = {constraints,equations of motion,multibody dynamics},
  language     = {eng},
  number       = {3},
  pages        = {209--242},
  publisher    = {SAGE Publications Inc.},
  series       = {Mathematics and Mechanics of Solids},
  title        = {On the equations of motion in constrained multibody dynamics},
  url          = {http://dx.doi.org/10.1177/1081286511407111},
  volume       = {17},
  year         = {2012},
}