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We analyze constrained quantum systems where the dynamics do not preserve the constraints. This is done in particular for the restriction of a quantum particle in Euclidean n-space to a curved submanifold, and we propose a method of…

High Energy Physics - Theory · Physics 2008-11-26 Hendrik Grundling , C. A. Hurst

A notion of implicit difference equation on a Lie groupoid is introduced and an algorithm for extracting the integrable part (backward or/and forward) is formulated. As an application, we prove that discrete Lagrangian dynamics on a Lie…

Differential Geometry · Mathematics 2011-04-04 D. Iglesias , J. C. Marrero , D. Martin de Diego , E. Padron

A scheme for generating a family of convex variational principles is developed, the Euler- Lagrange equations of each member of the family formally corresponding to the necessary conditions of optimal control of a given system of ordinary…

Optimization and Control · Mathematics 2025-06-13 Amit Acharya , Janusz Ginster

The Helmholtz conditions are necessary and sufficient conditions for a system of second order differential equations to be variational, that is, equivalent to a system of Euler-Lagrange equations for a regular Lagrangian. On the other hand,…

Optimization and Control · Mathematics 2018-10-17 Marta Farré Puiggalí , Anthony M. Bloch

A new geometric approach to systems with boundary energy flow is developed using infinite-dimensional Dirac structures within the Lagrangian formalism. This framework satisfies a list of consistency criteria with the geometric setting of…

Symplectic Geometry · Mathematics 2025-11-11 François Gay-Balmaz , Álvaro Rodríguez Abella , Hiroaki Yoshimura

In this paper we consider second-order field theories in a variational setting. From the variational principle the Euler-Lagrange equations follow in an unambiguous way, but it is well known that this is not true for the Cartan form. This…

Optimization and Control · Mathematics 2018-09-27 Markus Schöberl , Kurt Schlacher

We introduce a general method to construct classes of dynamical systems invariant under generalizations of the Carroll and of the Galilei groups. The method consists in starting from a space-time in $D+1$ dimensions and partitioning it in…

High Energy Physics - Theory · Physics 2018-10-31 Andrea Barducci , Roberto Casalbuoni , Joaquim Gomis

We study the relaxation of the bi-dimensional kinetically constrained spiral model. We show that due to the reversibility of the dynamic rules any unblocked state fully decorrelates in finite times irrespectively of the system being in the…

Statistical Mechanics · Physics 2009-09-28 Federico Corberi , Leticia F. Cugliandolo

We propose a novel algorithmic method for constructing invariant variational schemes of systems of ordinary differential equations that are the Euler-Lagrange equations of a variational principle. The method is based on the invariantization…

Numerical Analysis · Mathematics 2021-09-28 Alex Bihlo , James Jackaman , Francis Valiquette

We derive the equations of nonlinear electroelastostatics using three different variational formulations involving the deformation function and an independent field variable representing the electric character - considering either one of…

Classical Physics · Physics 2023-12-21 Prashant Saxena , Basant Lal Sharma

One unusual property of dynamic systems, whose state is characterized by a set of scalar dynamic variables satisfying a system of differential equations of a general form, is considered. This property is related to the behavior of equations…

General Relativity and Quantum Cosmology · Physics 2019-11-06 Sergey S. Kokarev

In this paper, we present a Lagrangian formalism for nonequilibrium thermodynamics. This formalism is an extension of the Hamilton principle in classical mechanics that allows the inclusion of irreversible phenomena in both discrete and…

Mathematical Physics · Physics 2015-10-06 François Gay-Balmaz , Hiroaki Yoshimura

In this paper, Lagrangian formalisms of Classical Mechanics was deduced on Kaehlerian manifold being geometric model of a generalized Lagrange space.Then, it was given two applications of complex Euler-Lagrange equations on mechanics…

Dynamical Systems · Mathematics 2009-02-25 Mehmet Tekkoyun , Erdal Ozusaglam , Ali Gorgulu

By a semi-Lagrangian change of coordinates, the hydrostatic Euler equations describing free-surface sheared flows is rewritten as a system of quasilinear equations, where stability conditions can be determined by the analysis of its…

A variational principle is further developed for out of equilibrium dynamical systems by using the concept of maximum entropy. With this new formulation it is obtained a set of two first-order differential equations, revealing the same…

Data Analysis, Statistics and Probability · Physics 2019-03-22 Mario J. Pinheiro

The difference variational bicomplex, which is the natural setting for systems of difference equations, is constructed and used to examine the geometric and algebraic properties of various systems. Exactness of the bicomplex gives a…

Mathematical Physics · Physics 2026-04-21 Linyu Peng , Peter E. Hydon

A new model for the drag coefficient of a sphere in a concentrated system is described. It is based upon a cell-averaged model for the Stokes regime combined with a physically motivated extrapolation to arbitrary Reynolds number. It can be…

Fluid Dynamics · Physics 2015-01-13 Gary Tupper , Indresan Govender , Aubrey Mainza

In this paper, we develop a Hamiltonian variational formulation for the nonequilibrium thermodynamics of simple adiabatically closed systems that is an extension of Hamilton's phase space principle in mechanics. We introduce the…

Mathematical Physics · Physics 2022-04-05 Hiroaki Yoshimura , François Gay-Balmaz

This paper presents a geometric description on Lie algebroids of Lagrangian systems subject to nonholonomic constraints. The Lie algebroid framework provides a natural generalization of classical tangent bundle geometry. We define the…

Mathematical Physics · Physics 2008-04-30 J. Cortes , M. de Leon , J. C. Marrero , E. Martinez

Linear and nonlinear Hodge-like systems for 1-forms are studied, with an assumption equivalent to complete integrability substituted for the requirement of closure under exterior differentiation. The systems are placed in a variational…

Analysis of PDEs · Mathematics 2010-12-21 Antonella Marini , Thomas H. Otway