Contact Hamiltonian Dynamics: The Concept And Its Use

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时滞是自然界和工程实践中常见的一种时间滞后现象, 对力学系统的动力学行为及基本性质都具有深刻的影响. Herglotz广义变分原理推广了经典变分原理, 可用于非保守系统的研究. 故利用Herglotz广义变分原理研究含时滞的非完整系统的对称性与守恒量在理论和应用上均具有重要意义. 文章将Herglotz型

Hamiltonian dynamics (CLASSICAL MECHANICS) | PDF

In this work, we devise a stochastic version of contact Hamiltonian systems and show that the phase flows of these systems preserve contact structures. Moreover, we provide a sufficient condition under which these stochastic contact Hamiltonian systems are completely integrable. This establishes an appropriate framework for investigating stochastic contact Full-text available Mar 2018 Matheus J. Lazo Juilson Paiva João T. S. Amaral Gastao S. F. Frederico Contact Hamiltonian Dynamics: The Concept and Its Use Article Full-text available Oct 2017 Entropy We propose a novel approach to contact Hamiltonian mechanics which, in contrast to the one dominating in the literature, serves also for non-trivial contact structures. In this approach

Formulation of stochastic contact Hamiltonian systems

In this paper, we continue to develop Aubry-Mather and weak KAM theories for contact Hamiltonian systems $ H(x,u,p) $ with certain dependence on the contact variable $ u $. For the Lipschitz dependence case, we obtain some properties of the Mañé set. For the non-decreasing case, we provide some information on the Aubry set, such as the comparison property, graph In this paper, we study Hamiltonian systems on contact manifolds, which is an appropriate scenario to discuss dissipative systems. We show how the dissipative dynamics can be interpreted as a Legendrian submanifold, and also prove a coisotropic reduction theorem similar to the one in symplectic mechanics; as a consequence, we get a method to reduce the Contact Hamiltonian system appears naturally in dissipative Hamiltonian mechanics [1, 2] as a natural extension of Hamiltonian mechanics [3,4], or in thermodynamics [5], mesoscopic dynamics [6

In this paper, we shall give new insights on dynamics of contact Hamiltonian flows, which are gaining importance in several branches of physics as they model a dissipative behaviour. We divide the contact phase space into three parts, which are corresponding to three differential invariant sets $ \\Omega_\\pm, \\Omega_0 $. On the invariant sets $ \\Omega_\\pm $, under We show that the contact dynamics obtained from the Herglotz variational principle can be described as a constrained nonholonomic or vakonomic ordinary Lagrangian system depending on a dissipative variable with an adequate choice of one constraint. As a consequence, we obtain the dynamics of contact nonholonomic and vakonomic systems as an Conclusion Hamiltonian mechanics is a cornerstone of modern engineering, offering a powerful framework for analyzing and designing dynamic systems. From its fundamental principles to its wide-ranging applications, Hamiltonian mechanics has proven to be an invaluable tool for engineers across various fields.

Abstract. This paper presents a systematic quantitative study of contact rigidity phenomena based on the contact Hamiltonian Floer theory established in [35]. Our quantitative approach applies to arbitrary admissible contact Hamiltonian functions on the contact boundary M = ∂W of a weakly+-monotone symplectic manifold W. From a theoretical standpoint, we develop a comprehensive

We give a short survey on the concept of contact Hamiltonian dynamics and its use in several areas of physics, namely reversible and irreversible thermodynamics, statistical physics and classical

Conformal and Contact Kinetic Dynamics and Their Geometrization

Contact Hamiltonian Mechanics
[1604.08266] Contact Hamiltonian Mechanics
Conformal and Contact Kinetic Dynamics and Their Geometrization
CONTACT HAMILTONIAN SYSTEMS

Equations (1)are the equations of motion for the system from contact Hamiltonian dynamics, which is a natural extension of Hamiltonian dynamics [1].

an be de ned straightforward. This work gives a concise and short survey of the concept of contact Hamiltonian dynamics and its application in classical dissipative system, enhancing the fact that this theory includes all the important pro erties of the symplectic one. Besides, along this discussion, we provide examples which enable In this work we devise a stochastic version of contact Hamiltonian systems, and show that the phase flows of these systems preserve contact structures. Moreover, we provide a sufficient condition under which these stochastic contact Hamiltonian systems are completely integrable. This establishes an appropriate framework for investigating stochastic contact Hamiltonian

ESSENTIALS OF HAMILTONIAN DYNAMICS Classical dynamics is one of the cornerstones of advanced education in physics and applied mathematics, with applications across engineering, chemistry, and biology. In this book, the author uses a concise and pedagogical style to cover all the topics necessary for a graduate-level course in dynamics based on Hamiltonian methods. In physics, Hamiltonian mechanics is a reformulation of Lagrangian mechanics that emerged in 1833. Introduced by the Irish mathematician Sir William Rowan Hamilton, [1] Hamiltonian mechanics replaces (generalized) velocities used in Lagrangian mechanics with (generalized) momenta. Both theories provide interpretations of classical mechanics and describe the same A short survey on the concept of contact Hamiltonian dynamics and its use in several areas of physics, namely reversible and irreversible thermodynamics, statistical physics and classical mechanics, and insights into possible future directions are given.

As the initial research of contact Hamiltonian dynamics in this direction, we investigate the dynamics of contact Hamiltonian systems in some special cases including invariants, completeness of phase flows and periodic behavior. In this paper we study vakonomic dynamics on contact systems with nonlinear constraints. In order to obtain the dynamics, we consider a space of admisible paths, which are the ones tangent to a given submanifold. Then, we find the critical points of the Herglotz We give a short survey on the concept of contact Hamiltonian dynamics and its use in several areas of physics, namely reversible and irreversible thermodynamics, statistical physics and classical

Crossref Google Scholar [3] Bravetti A Contact Hamiltonian dynamics: the concept and its use Entropy 2017 19 10 678 Crossref Google Scholar [4] Indeed, these control problems can be considered as particular cases of vakonomic contact systems, and we can use the Lagrangian theory of contact systems in order to understand their symmetries and dynamics. Keywords: Contact Hamiltonian systems, Constrained systems, Vakonomic dynamics, Optimal Control.

We propose a conformal generalization of the reversible Vlasov equation of kinetic plasma dynamics, called conformal kinetic theory. In order to arrive at this formalism, we start with the conformal Hamiltonian dynamics of particles and lift it to the dynamical formulation of the associated kinetic theory. The resulting theory represents a simple example of a geometric Our quantitative approach applies to arbitrary admissible contact Hamiltonian functions on the contact boundary M=∂W??M=\partial Witalic_M = ∂ italic_Wof a weakly+-monotone symplectic manifold W?Witalic_W. From a theoretical standpoint, we develop a comprehensive contact spectral invariant theory. In this work we introduce contact Hamiltonian mechanics, an extension of symplectic Hamiltonian mechanics, and show that it is a natural candidate for a geometric description of non-dissipative and dissipative systems. For this purpose we review in detail the major features of standard symplectic Hamiltonian dynamics and show that all of them can be

Contact symmetries and Hamiltonian thermodynamics

4. A. Bravetti, Contact Hamiltonian dynamics: The concept and its use, Entropy 19(12) (2017) 535. Crossref, Web of Science, Google Scholar 7. R. Cawley, Determination We give a short survey on the concept of contact Hamiltonian dynamics and its use in several areas of physics, namely reversible and As the initial research of contact Hamiltonian dynamics in this direction, we investigate the dynamics of contact Hamiltonian systems in some special cases including invariants, completeness of phase flows and periodic behavior.

Jun Yan Contact Hamiltonian Dynamics: The Concept and Its Use Article Full-text available Oct 2017 Entropy Alessandro Bravetti Aubry-Mather Theory for Conformally Symplectic Systems Article Full We give a short survey on the concept of contact Hamiltonian dynamics and its use in several areas of physics, namely reversible and irreversible thermodynamics, statistical physics and classical

Abstract We propose a novel approach to contact Hamiltonian mechanics which, in contrast to the one dominating in the literature, serves also for non-trivial contact structures. In this section, after a brief review of the main aspects of contact Hamiltonian dynamics, we use these concepts to introduce a Hamiltonian function on the TPS whose flow defines thermodynamic processes. For this class of Hamiltonian systems Hessian and information geometric formulation is given. With this formulation, a generalized Toda’s dual transform is proposed, where his original transform was used in deriving his integrable lattice system.

We present a unified geometric framework for describing both the Lagrangian and Hamiltonian formalisms of contact autonomous mechanical systems, which is based on the approach of the pionnering

We give a short survey on the concept of contact Hamiltonian dynamics and its use in several areas of physics, namely reversible and irreversible thermodynamics, statistical physics and classical

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