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Related papers: A note on holonomic costraints

200 papers

We study thermodynamical formalism of a discrete nonautonomous dynamical system determined by a sequence of continuous self-maps of a compact metric space. Using the methods of Convex Analysis we get variational principles for pressure…

Dynamical Systems · Mathematics 2026-03-10 Andrzej Biś

In this paper we study a Hamiltonization procedure for mechanical systems with velocity-depending (nonholonomic) constraints. We first rewrite the nonholonomic equations of motion as Euler-Lagrange equations, with a Lagrangian that follows…

Mathematical Physics · Physics 2011-05-27 T. Mestdag , A. M. Bloch , O. E. Fernandez

A methodology for deriving dual variational principles for the classical Newtonian mechanics of mass points in the presence of applied forces, interaction forces, and constraints, all with a general dependence on particle velocities and…

Mathematical Physics · Physics 2024-07-02 Amit Acharya , Ambar N. Sengupta

This note presents an attempt to provide a conceptual framework for variational formulations of classical physics. Variational principles of physics have all a common source in the {\it principle of virtual work} well known in statics of…

Mathematical Physics · Physics 2007-05-23 Wlodzimierz M. Tulczyjew

We derive a collisionless kinetic theory for an ensemble of molecules undergoing nonholonomic rolling dynamics. We demonstrate that the existence of nonholonomic constraints leads to problems in generalizing the standard methods of…

Chaotic Dynamics · Physics 2013-02-26 Darryl D. Holm , Vakhtang Putkaradze , Cesare Tronci

A hybrid system is a system whose dynamics is given by a mixture of both continuous and discrete transitions. In particular, these systems can be utilised to describe the dynamics of a mechanical system with impacts. Based on the approach…

Mathematical Physics · Physics 2024-08-21 Leonardo Colombo , Manuel de León , María Emma Eyrea Irazú , Asier López-Gordón

Helicity plays a unique role as an integral invariant of a dynamical system. In this paper, the concept of helicity in the general setting of Hamiltonian dynamics is discussed. It is shown, through examples, how the conservation of overall…

Classical Physics · Physics 2024-02-14 Michael E. Glinsky , Poul G. Hjorth

In this paper we study optimal control problems for nonholonomic systems defined on Lie algebroids by using quasi-velocities. We consider both kinematic, i.e. systems whose cost functional depends only on position and velocities, and…

Optimization and Control · Mathematics 2015-05-27 L. Abrunheiro , M. Camarinha , J. F. Cariñena , J. Clemente-Gallardo , E. Martínez , P. Santos

The main topic of this work concerns the formulation of the equations of motion and the consequent energy balance that they imply for this type of systems, In particular, the analytical development that we will carry out on the equations of…

Classical Physics · Physics 2023-04-25 Federico Talamucci

A holonomic constraint is used to enforce a constant instantaneous configurational temperature on an equilibrium system. Three sets of equations of motion are obtained, differing according to the way in which the holonomic constraint is…

Statistical Mechanics · Physics 2007-06-13 Igor Rychkov , Debra J. Searles

A new approach to relativistic mechanics is proposed, suitable to describe dynamics of different kinds of relativistic particles. Mathematically it is based on an application of the recent geometric theory of nonholonomic systems on fibred…

Mathematical Physics · Physics 2009-04-21 Olga Krupkova , Jana Musilova

We study relations between vakonomically and nonholonomically constrained Lagrangian dynamics for the same set of linear constraints. The basic idea is to compare both situations at the level of variational principles, not equations of…

Differential Geometry · Mathematics 2019-02-01 Michał Jóźwikowski , Witold Respondek

The confusion and ambiguity encountered by students, in understanding virtual displacement and virtual work, is discussed in this article. A definition of virtual displacement is presented that allows one to express them explicitly for…

Physics Education · Physics 2009-11-11 Subhankar Ray , J. Shamanna

Non-conservative loads of the follower type are usually believed to be the source of dynamic instabilities such as flutter and divergence. It is shown that these instabilities (including Hopf bifurcation, flutter, divergence, and…

Classical Physics · Physics 2024-01-05 Alessandro Cazzolli , Francesco Dal Corso , Davide Bigoni

This paper presents a formulation of Lagrangian dynamics of constrained mechanical systems in terms of reduced quasi-velocities and quasi-forces that can be used for simulation, analysis, and control purposes. In this formulation, Cholesky…

Computational Physics · Physics 2021-08-17 Farhad Aghili

We discuss an extension of the Hamilton-Jacobi theory to nonholonomic mechanics with a particular interest in its application to exactly integrating the equations of motion. We give an intrinsic proof of a nonholonomic analogue of the…

Mathematical Physics · Physics 2011-08-15 Tomoki Ohsawa , Anthony M. Bloch

In this study, it is generalized the concept of Lagrangian mechanics with constraints to complex case. To be beginning, it is considered a Kaehlerian manifold as a velocity-phase space. Then a non-holonomic constraint is given by 1-form on…

Differential Geometry · Mathematics 2009-02-25 Mehmet Tekkoyun , Ali Gorgulu

In this paper, we present a collection of infinite-dimensional systems with nonholonomic constraints. In finite dimensions the two essentially different types of dynamics, nonholonomic or vakonomic ones, are known to be obtained by taking…

Differential Geometry · Mathematics 2026-04-10 Alexander G. Abanov , Boris Khesin

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

We propose a first example of a simple classical field theory with nonholonomic constraints. Our model is a straightforward modification of a Cosserat rod. Based on a mechanical analogy, we argue that the constraint forces should be modeled…

Mathematical Physics · Physics 2007-05-23 Joris Vankerschaver