A generalized geometric framework for constrained systems
type: Item
instance of: scholarly article
title: A generalized geometric framework for constrained systems
zbMATH Open document ID: 0763.34001
DOI: 10.1016/0926-2245(92)90012-C
author: X. Gràcia
author: J. M. Pons
published in: Differential Geometry and its Applications
publication date: 1993-02-10T00:00:00Z
review text: A geometric framework for constrained dynamical systems of the form \(A(x)x'=F(x)\) is presented. The framework is used to describe a general type of first order differential equations on a manifold. In this paper these systems are called linearly constrained systems. A stabilization algorithm is devised and discussed in order to solve the equation of motion. The formalism includes the presymplectic and Lagrangian formalisms as well as higher order Lagrangians. In numerical analysis the system \(A(x)x'=F(x)\) is called a linearly implicit differential algebraic equation (DAE). The stabilization algorithm of this paper consists of the construction of a sequence of manifolds. This is very similar to the recent constructions of Rabier, Reich, and Rheinboldt developed in the numerical analysis literature of DAEs.
reviewed by: Stephen L. Campbell
Mathematics Subject Classification ID: 34A09
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 70H05
zbMATH DE Number: 118414
zbMATH Keywords: DAE
zbMATH Keywords: geometric framework
zbMATH Keywords: constrained dynamical systems
zbMATH Keywords: first order differential equations on a manifold
zbMATH Keywords: stabilization algorithm
zbMATH Keywords: presymplectic and Lagrangian formalisms
zbMATH Keywords: higher order Lagrangians
zbMATH Keywords: linearly implicit differential algebraic equation
Wikidata QID: Q115362757
MaRDI profile type: Publication
cites work: Q4174811
cites work: Manifolds, tensor analysis, and applications.
cites work: Equivalence between the Lagrangian and Hamiltonian formalism for constrained systems
cites work: The Hamiltonian structure of Yang-Mills theories and instantons. I
cites work: Q5557748
cites work: Q3852479
cites work: On constrained mechanical systems: D’Alembert’s and Gauss’ principles
cites work: The time-evolution operator for singular Lagrangians
cites work: Higher-order differential equations and higher-order lagrangian mechanics
cites work: Q5610453
cites work: Foundations of Quantum Mechanics
cites work: Presymplectic manifolds and the Dirac–Bergmann theory of constraints
cites work: Q3049554
cites work: Q3900713
cites work: On an evolution operator connecting Lagrangian and Hamiltonian formalisms
cites work: Constrained systems: A unified geometric approach
cites work: Higher-order Lagrangian systems: Geometric structures, dynamics, and constraints
cites work: Higher-order conditions for singular Lagrangian dynamics
cites work: Q3702989
cites work: Q4692932
cites work: Q3785520
cites work: Q4076834
cites work: Reduction of symplectic manifolds with symmetry
cites work: Q4191318
cites work: Hamiltonian systems with constraints: a geometric approach
cites work: Q4015798
cites work: New relations between Hamiltonian and Lagrangian constraints
cites work: Ostrogradski's theorem for higher-order singular Lagrangians
cites work: Differential-Algebraic Systems as Differential Equations on Manifolds
cites work: Q3994886
cites work: First-order equations of motion for classical mechanics
cites work: Generalized Hamiltonian dynamics. I. Formulation on T*Q⊕T Q
cites work: Q4048647
cites work: Hamiltonian systems with constraints and their meaning in mechanics
full work available at URL: 0926-2245(92)90012-c
OpenAlex ID: W2007352075
description: scientific article; zbMATH DE number 118414