Related papers: Continuous and discrete damping reduction for syst…
In this paper, we make a generalization of Routh's reduction method for Lagrangian systems with symmetry to the case where not any regularity condition is imposed on the Lagrangian. First, we show how implicit Lagrange-Routh equations can…
Using an effective Hamiltonian including the Zeeman and internal interactions, we describe the quantum theory of magnetization dynamics when the spin system evolves non-adiabatically and out of equilibrium. The Lewis-Riesenfeld dynamical…
It is well known that the Lagrangian and Hamiltonian descriptions of field theories are equivalent at the discrete time level when variational integrators are used. Besides the symplectic Hamiltonian structure, many physical systems exhibit…
In this paper a new approach is proposed to quantize mechanical systems whose equations of motion can not be put into Hamiltonian form. This approach is based on a new type of variational principle, which is adopted to a describe a…
The relationship between the Hamiltonian and Lagrangean functions in analytical mechanics is a type of duality. The two functions, while distinct, are both descriptive functions encoding the behavior of the same dynamical system. One…
The discretization approximation method commonly used to simulate the dynamics of quantum system coupled to the environment in continuum often suffers from the periodically partial recovery of initial state because of the effect of finite…
In this paper, we introduce a geometric description of contact Lagrangian and Hamiltonian systems on Lie algebroids in the framework of contact geometry, using the theory of prolongations. We discuss the relation between Lagrangian and…
In purely non-dissipative systems, Lagrangian and Hamiltonian reduction have proven to be powerful tools for deriving physical models with exact conservation laws. We have discovered a hint that an analogous reduction method exists also for…
In this paper we propose a process of lagrangian reduction and reconstruction for nonholonomic discrete mechanical systems where the action of a continuous symmetry group makes the configuration space a principal bundle. The result of the…
We introduce a data-driven method for learning the equations of motion of mechanical systems directly from position measurements, without requiring access to velocity data. This is particularly relevant in system identification tasks where…
The Caldeira-Leggett Hamiltonian (Eq. (1) below) describes the interaction of a discrete harmonic oscillator with a continuous bath of harmonic oscillators. This system is a standard model of dissipation in macroscopic low temperature…
In this paper, we survey our recent results on the variational formulation of nonequilibrium thermodynamics for the finite dimensional case of discrete systems as well as for the infinite dimensional case of continuum systems. Starting with…
This essay advocates the view that any problem that has a meaningful empirical content, can be formulated in constructive, more definitely, finite terms. We consider combinatorial models of dynamical systems and approaches to statistical…
An interesting family of geometric integrators for Lagrangian systems can be defined using discretizations of the Hamilton's principle of critical action. This family of geometric integrators is called variational integrators. In this…
In this paper we present a general framework that allows one to study discretization of certain dynamical systems. This generalizes earlier work on discretization of Lagrangian and Hamiltonian systems on tangent bundles and cotangent…
In this paper, a new approach for constructing Lagrangians for driven and undriven linearly damped systems is proposed, by introducing a redefined time coordinate and an associated coordinate transformation to ensure that the resulting…
In this paper an approach is proposed to represent a class of dissipative mechanical systems by corresponding infinite-dimensional Hamiltonian systems. This approach is based upon the following structure: for any non-conservative classical…
The recent interest in structure preserving stochastic Lagrangian and Hamiltonian systems raises questions regarding how such models are to be understood and the principles through which they are to be derived. By considering a…
For the linearized setting of the dynamics of complex bodies we construct variational integrators and prove their convergence by making use of BV estimates on the rate fields. We allow for peculiar substructural inertia and internal…
In this paper we study the coisotropic reduction in different types of dynamics according to the geometry of the corresponding phase space. The relevance of the coisotropic reduction is motivated by the fact that these dynamics can always…