Composite variational principles, added variables, and constants of motion
type: Item
instance of: scholarly article
title: Composite variational principles, added variables, and constants of motion
zbMATH Open document ID: 0608.34053
DOI: 10.1007/BF00677702
author: Giacomo Caviglia
published in: International Journal of Theoretical Physics
publication date: 1986-01-01T00:00:00Z
review text: It is shown that any second order differential system admits a variational formulation via the introduction of suitable additional variables. The new variables are related to the existence of invariant 1- forms and to solutions for the adjoint of the equations of variation of the given system. The connections among invariant forms, constants of motion, and infinitesimal invariance transformations are then discussed in some detail.
Mathematics Subject Classification ID: 34C99
Mathematics Subject Classification ID: 49J15
zbMATH DE Number: 3983671
zbMATH Keywords: second order differential system
zbMATH Keywords: invariant forms
MaRDI profile type: Publication
cites work: Mixed variational principles for some non-self-adjoint dynamical systems
cites work: Dynamical symmetries: An approach to Jacobi fields and to constants of geodesic motion
cites work: Dynamical symmetries of the geodesic equation
cites work: Dynamical symmetries, first integrals and the inverse problem of Lagrangian dynamics
cites work: Helmholtz conditions, covariance, and invariance identities
cites work: On the differential geometry of the Euler-Lagrange equations, and the inverse problem of Lagrangian dynamics
cites work: On the inverse problem of the calculus of variations
cites work: Q5821083
cites work: Projective differential geometry and geodesic conservation laws in general relativity. I: Projective actions
cites work: Q4185862
cites work: Generalizations of Noether’s Theorem in Classical Mechanics
cites work: Dual Variational Principles for a Class of Non-linear Partial Differential Equations
cites work: Lagrangian mechanics and the geometry of configuration spacetime
description: scientific article; zbMATH DE number 3983671