Application of graph theory to the determination of potential energy of systems consisting of rigid bodies and springs
type: Item
instance of: scholarly article
title: Application of graph theory to the determination of potential energy of systems consisting of rigid bodies and springs
zbMATH Open document ID: 0659.70002
DOI: 10.1016/0016-0032(87)90049-4
published in: Journal of the Franklin Institute
publication date: 1987-01-01T00:00:00Z
review text: This paper follows a previous study of the author [ibid. 324, 351-367 (1987; Zbl 0643.70002)] on the application of graph theory to the determination of kinetic energy of rigid body systems. The potential energy of a system consisting of rigid bodies is calculated in a systematic manner using a graph theoretical method. The notations are those of \textit{J. Wittenburg} [Dynamics of systems of rigid bodies (1977; Zbl 0363.70004)] and it is assumed that the system has a topological tree structure. Two kinds of problems are considered: the potential energy of gravity forces and the potential energy of springs. The main aim of this paper is the calculation of the potential energy of a system of rigid bodies connected by a system of simple linear translational springs. In this case, two graphs are needed at the same time, one displays the interconnection structure of the system of solids by the hinges, the other displays the topological structure of the system of linear springs. The general formula for the potential energy is derived. Implementation is performed in the case of planar systems and an example is provided.
Mathematics Subject Classification ID: 70B15
Mathematics Subject Classification ID: 68R10
Mathematics Subject Classification ID: 94C15
zbMATH DE Number: 4078867
zbMATH Keywords: application of graph theory
zbMATH Keywords: kinetic energy of rigid body systems
zbMATH Keywords: topological tree structure
zbMATH Keywords: potential energy of gravity forces
zbMATH Keywords: potential energy of springs
zbMATH Keywords: simple linear translational springs
author: Krzysztof Arczewski
reviewed by: Thérèse Lévy
MaRDI profile type: Publication
full work available at URL: 0016-0032(87)90049-4
OpenAlex ID: W2071267113
cites work: Q4138203
cites work: Application of graph theory to the determination of kinetic energy of rigid body systems
cites work: Determination of Christoffel symbols of the first kind for a class of rigid body systems by topological considerations
cites work: Q5734115
cites work: Q3263386
cites work: Q3232806
cites work: Q4088840
description: scientific article; zbMATH DE number 4078867