Related papers: When action is not least for systems with action-d…
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…
Invariant conditions for conformable fractional problems of the calculus of variations under the presence of external forces in the dynamics are studied. Depending on the type of transformations considered, different necessary conditions of…
Dynamical chaos has recently been shown to exist in the Gaussian approximation in quantum mechanics and in the self-consistent mean field approach to studying the dynamics of quantum fields. In this study, we first show that any variational…
It is shown that a given non-autonomous system of two first-order ordinary differential equations can be expressed in Hamiltonian form. The derivation presented here allow us to obtain previously known results such as the infinite number of…
We are able to derive the equations of motion for forced mechanical systems in a purely variational setting, both in the context of Lagrangian or Hamiltonian mechanics, by duplicating the variables of the system as introduced by Galley…
We derive the dynamics of several rigid bodies of arbitrary shape in a 2-dimensional inviscid and incompressible fluid, whose vorticity field is given by point vortices. We adopt the idea of Vankerschaver et al. (2009) to derive the…
Field equations with time and coordinates derivatives of noninteger order are derived from stationary action principle for the cases of power-law memory function and long-range interaction in systems. The method is applied to obtain a…
A variational integrator for ideal magnetohydrodynamics is derived by applying a discrete action principle to a formal Lagrangian. Discrete exterior calculus is used for the discretisation of the field variables in order to preserve their…
In ergodic quantum systems, physical observables have a non-relaxing component if they "overlap" with a conserved quantity. In interacting microscopic models, how to isolate the non-relaxing component is unclear. We compute exact dynamical…
In this article we address the question whether it is possible to learn the differential equations describing the physical properties of a dynamical system, subject to non-conservative forces, from observations of its realspace…
The notion of fractional dynamics is related to equations of motion with one or a few terms with derivatives of a fractional order. This type of equation appears in the description of chaotic dynamics, wave propagation in fractal media, and…
We study the constrained Ostrogradski-Hamilton framework for the equations of motion provided by mechanical systems described by second-order derivative actions with a linear dependence in the accelerations. We stress out the peculiar…
Some problems on variations are raised for classical discrete mechanics and field theory and the difference variational approach with variable step-length is proposed motivated by Lee's approach to discrete mechanics and the difference…
Fractional action-like variational problems have recently gained importance in studying dynamics of nonconservative systems. In this note we address multi-dimensional fractional action-like problems of the calculus of variations.
We propose a method for learning dynamical systems from high-dimensional empirical data that combines variational autoencoders and (spatio-)temporal attention within a framework designed to enforce certain scientifically-motivated…
In this paper we develop a fractional Hamiltonian formulation for dynamic systems defined in terms of fractional Caputo derivatives. Expressions for fractional canonical momenta and fractional canonical Hamiltonian are given, and a set of…
It is well known that the equations of motion obtained from Newtons second law of motion can be obtained from a Lagrangian via the Euler-Lagrangian formulation if and only if the equations of motion satisfy the Helmholtz conditions. In this…
Stochastic field theories are often constructed phenomenologically, without a systematic assessment of thermodynamic consistency or local detailed balance. This may hinder a physical description of irreversibility at the field-theoretic…
We apply the approximate dynamics derived from the Gaussian time-dependent variational principle to the Hamiltonian $ \hat H= {1/2}(\hat p_x ^2+ \hat p_y ^2)+ {1/2}\hat x^2\hat y^2$, which is strongly chaotic in the classical limit. We are…
We reconsider the variational integration of optimal control problems for mechanical systems based on a direct discretization of the Lagrange-d'Alembert principle. This approach yields discrete dynamical constraints which by construction…