Application of graph theory to the determination of kinetic energy of rigid body systems
type: Item
instance of: scholarly article
title: Application of graph theory to the determination of kinetic energy of rigid body systems
zbMATH Open document ID: 0643.70002
DOI: 10.1016/0016-0032(87)90048-2
published in: Journal of the Franklin Institute
publication date: 1987-01-01T00:00:00Z
review text: This paper extends the studies of \textit{J. Wittenburg} on: (*) ``Dynamics of systems of rigid bodies'' (1977; Zbl 0363.70004) using the graph theory. An important problem in the dynamic analysis of mechanical systems is the determination of the Lagrangian and specially of the kinetic energy. The author presents a new method for the calculation of the kinetic energy for a system of N rigid bodies having a tree structure (*), by mean of the graph theory. Expression of the kinetic energy is obtained in terms of the translational velocities \(\vec u_ i\) and rotational velocities \({\vec \omega}_ i\) \((i=1,...,N)\) of the solids. This expression contains essential system data (i.e. inertia characteristics and locations of certain points within the system) and the topological informations by means of the path matrix \(P^{(1)}\). This approach offers a systematic expression which can be used for many different systems. Detailed calculations are performed in the case of planar motion.
Mathematics Subject Classification ID: 70B15
Mathematics Subject Classification ID: 68R10
Mathematics Subject Classification ID: 94C15
zbMATH DE Number: 4049175
zbMATH Keywords: kinetic energy of rigid body systems
zbMATH Keywords: six degree-of-freedom rigid body system
zbMATH Keywords: tree structure
zbMATH Keywords: graph theory
zbMATH Keywords: path matrix
zbMATH Keywords: planar motion
author: Krzysztof Arczewski
reviewed by: Thérèse Lévy
MaRDI profile type: Publication
full work available at URL: 0016-0032(87)90048-2
OpenAlex ID: W1993952347
cites work: Q4138203
cites work: Determination of Christoffel symbols of the first kind for a class of rigid body systems by topological considerations
description: scientific article; zbMATH DE number 4049175