The dynamics of rheonomic Lagrangian systems with constraints
type: Item
instance of: scholarly article
title: The dynamics of rheonomic Lagrangian systems with constraints
zbMATH Open document ID: 0575.70016
DOI: 10.1016/0021-8928(84)90002-9
author: V. V. Rumyantsev
published in: Journal of Applied Mathematics and Mechanics
publication date: 1985-01-01T00:00:00Z
review text: General rheonomic Lagrangian systems with non-integrale constraints are considered. Their equations of motion, in the form of the Lagrange equations with multipliers, are equivalent to the variational equation expressing the Hamilton principle in Hölder form, which occurs when determining the synchronous Chetaev variations. A parametric study of the motions of such systems is made in the extended configurational space \({\mathbb{R}}^{n+1}\) with arbitrarily chosen parameters. When the Lagrangian is independent of t and the constraints are homogeneous with respect to the velocities, the equations of motion have an energy integral corresponding to the ignorable coordinate t. The energy integral is used to reduce the order of the initial equations, and a generalization of the Jacobi-Whittaker equations is obtained as a result.
Mathematics Subject Classification ID: 70H25
zbMATH DE Number: 3919885
zbMATH Keywords: principle of least action
zbMATH Keywords: anholonomic constraints
zbMATH Keywords: Lagrange multipliers
zbMATH Keywords: rheonomic Lagrangian systems
zbMATH Keywords: non-integrale constraints
zbMATH Keywords: Hamilton principle in Hölder form
zbMATH Keywords: synchronous Chetaev variations
zbMATH Keywords: extended configurational space
zbMATH Keywords: energy integral
zbMATH Keywords: Jacobi-Whittaker equations
MaRDI profile type: Publication
full work available at URL: 0021-8928(84)90002-9
OpenAlex ID: W1982426629
cites work: Q3873622
cites work: Q5729749
cites work: Q4188801
cites work: Q5636342
cites work: Q5512814
cites work: Q4935312
cites work: Q3219811
cites work: On stability of motion of nonholonomic systems
cites work: Q5184441
description: scientific article; zbMATH DE number 3919885