Coordinate representations for rigid parts in multibody dynamics
(2016) In Mathematics and Mechanics of Solids 21(8). p.9901025 Abstract
The paper is concerned with coordinate representations for rigid parts in multibody dynamics. The discussion is based on the general theory of the dynamics of multibody systems under constraints. General configuration coordinates are introduced and the requirement of their regularity is discussed. The use of Euler angles, quaternions and linear coordinates, where quaternions and linear coordinates require constraint conditions, is analysed in detail. These coordinate systems are all shown to be regular. Equations of motion are formulated, using Lagrange's as well as Euler's equations, and they are supplemented by the appropriate constraint conditions in the cases of quaternions and linear coordinates. Mass matrices are derived, and in... (More)
The paper is concerned with coordinate representations for rigid parts in multibody dynamics. The discussion is based on the general theory of the dynamics of multibody systems under constraints. General configuration coordinates are introduced and the requirement of their regularity is discussed. The use of Euler angles, quaternions and linear coordinates, where quaternions and linear coordinates require constraint conditions, is analysed in detail. These coordinate systems are all shown to be regular. Equations of motion are formulated, using Lagrange's as well as Euler's equations, and they are supplemented by the appropriate constraint conditions in the cases of quaternions and linear coordinates. Mass matrices are derived, and in terms of the Euler angles the mass matrix components are products of trigonometric functions whereas in terms of quaternions the matrix components are quadratic polynomials. Using linear coordinates gives rise to a constant mass matrix. Thus, there is a decreasing degree of complexity, regarding mass matrix components, when going from Euler angles to linear coordinates. This is obtained at the expense of an increasing gross number of degrees of freedom and the necessary introduction of constraint conditions. The different equations of motion obtained are compared with respect to their structural complexity. In all representations the components of the angular velocity are explicitly calculated. This is not always the case in previous investigations of this subject. The paper also gives a new proof of the wellknown relation between angular velocity and unit quaternions and their time derivative.
(Less)
 author
 AfzaliFar, B. ^{LU} and Lidström, P. ^{LU}
 organization
 publishing date
 20160901
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 configuration coordinates, equations of motion, Euler angles, linear coordinates, Multibody dynamics, quaternions, rigid body, rotation tensor
 in
 Mathematics and Mechanics of Solids
 volume
 21
 issue
 8
 pages
 36 pages
 publisher
 SAGE Publications
 external identifiers

 Scopus:84983028239
 WOS:000382845200005
 ISSN
 17413028
 DOI
 10.1177/1081286514546180
 language
 English
 LU publication?
 yes
 id
 3f169822e9b64d0cac290afa8bdd1367 (old id 7863092)
 date added to LUP
 20160126 14:39:39
 date last changed
 20170101 08:17:51
@article{3f169822e9b64d0cac290afa8bdd1367, abstract = {<p>The paper is concerned with coordinate representations for rigid parts in multibody dynamics. The discussion is based on the general theory of the dynamics of multibody systems under constraints. General configuration coordinates are introduced and the requirement of their regularity is discussed. The use of Euler angles, quaternions and linear coordinates, where quaternions and linear coordinates require constraint conditions, is analysed in detail. These coordinate systems are all shown to be regular. Equations of motion are formulated, using Lagrange's as well as Euler's equations, and they are supplemented by the appropriate constraint conditions in the cases of quaternions and linear coordinates. Mass matrices are derived, and in terms of the Euler angles the mass matrix components are products of trigonometric functions whereas in terms of quaternions the matrix components are quadratic polynomials. Using linear coordinates gives rise to a constant mass matrix. Thus, there is a decreasing degree of complexity, regarding mass matrix components, when going from Euler angles to linear coordinates. This is obtained at the expense of an increasing gross number of degrees of freedom and the necessary introduction of constraint conditions. The different equations of motion obtained are compared with respect to their structural complexity. In all representations the components of the angular velocity are explicitly calculated. This is not always the case in previous investigations of this subject. The paper also gives a new proof of the wellknown relation between angular velocity and unit quaternions and their time derivative.</p>}, author = {AfzaliFar, B. and Lidström, P.}, issn = {17413028}, keyword = {configuration coordinates,equations of motion,Euler angles,linear coordinates,Multibody dynamics,quaternions,rigid body,rotation tensor}, language = {eng}, month = {09}, number = {8}, pages = {9901025}, publisher = {SAGE Publications}, series = {Mathematics and Mechanics of Solids}, title = {Coordinate representations for rigid parts in multibody dynamics}, url = {http://dx.doi.org/10.1177/1081286514546180}, volume = {21}, year = {2016}, }