The equations of Lagrange written for a non-material volume
type: Item
instance of: scholarly article
title: The equations of Lagrange written for a non-material volume
zbMATH Open document ID: 1029.70006
DOI: 10.1007/BF01177454
published in: Acta Mechanica
publication date: 2004-01-25T00:00:00Z
review text: The authors consider a continuous body whose motion is dependent on a finite set of generalised coordinates. Then they extend classical Lagrange equations involving the total kinetic energy of the body with respect to a non-material control volume which coincides instantaneously with the material volume. The authors employ the well-known formalism of continuum mechanics to show that the extended Lagrange equations must additionally contain some integrals over the boundary of the body which are originated by differences of velocities on coinciding material and non-material surfaces. The Lagrange equations so obtained are employed to derive the equations governing the rectilinear motion of a rocket and the falling of a folded string hanged vertically down from a fixed point.
Mathematics Subject Classification ID: 70H03
zbMATH DE Number: 1757439
zbMATH Keywords: extended Lagrange equations
zbMATH Keywords: generalised coordinates
zbMATH Keywords: total kinetic energy
zbMATH Keywords: non-material control volume
zbMATH Keywords: continuum mechanics
zbMATH Keywords: rectilinear motion of rocket
zbMATH Keywords: falling of folded string
author: H. Irschik
author: H. J. Holl
reviewed by: Erdoğan S. Şuhubi
MaRDI profile type: Publication
cites work: Q4002437
cites work: Q4223034
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cites work: Q4528996
full work available at URL: https://doi.org/10.1007/bf01177454
OpenAlex ID: W2079249618
description: scientific article; zbMATH DE number 1757439