Related papers: A conceptual approach to the problem of action-ang…
Connections between the principle of stationary action and optimal control, and between established notions of minimax and viscosity solutions, are combined to describe trajectories of energy conserving systems as solutions of corresponding…
We proved the existence of invariant tori in differentiable Hamiltonian vector fields without action-angle variables. It is a generalization of the result of [Llave, 2005] that deals with analytic vector fields.
We investigate the large-time behavior of the value functions of the optimal control problems on the $n$-dimensional torus which appear in the dynamic programming for the system whose states are governed by random changes. From the point of…
We formulate a stochastic least-action principle for solutions of the incompressible Navier-Stokes equation, which formally reduces to Hamilton's principle for the incompressible Euler solutions in the case of zero viscosity. We use this…
A key issue in dimension reduction of dissipative dynamical systems with spectral gaps is the identification of slow invariant manifolds. We present theoretical and numerical results for a variational approach to the problem of computing…
We define a new dynamical variable, the relative existence e, in terms of space and time. Taking it as a generalized positional coordinate, we show that for conservative systems the canonically conjugated momentum is identified as the…
We present, for the first time, an action principle that gives the equations of motion of an extended body possessing multipole moments in an external gravitational field, in the weak field limit. From the action, the experimentally…
In this work, we propose an Action Principle for Action-dependent Lagrangian functions by generalizing the Herglotz variational problem to the case with several independent variables. We obtain a necessary condition for the extremum…
We study a family of dynamical systems obtained by coupling an Anosov map on the two-dimensional torus -- the chaotic system -- with the identity map on the one-dimensional torus -- the neutral system -- through a dissipative interaction.…
Flexibility and rigidity properties of steady (time-independent) solutions of the Euler, Boussinesq and Magnetohydrostatic equations are investigated. Specifically, certain Liouville-type theorems are established which show that suitable…
In this note, we propose a novel approach for a class of autonomous dynamical systems that allows, given some observations of the solutions, to identify its parameters and reconstruct the state vector. This approach relies on proving the…
The fractional Sturm-Liouville eigenvalue problem appears in many situations, e.g., while solving anomalous diffusion equations coming from physical and engineering applications. Therefore to obtain solutions or approximation of solutions…
It is argued that the world is a dissipative dynamic system, a phase flow of which is formed by conformally-symplectic mapping. The key assumption is that the concept of energy in microcosm makes sense only for the steady motions…
The principle of least action, a fundamental principle in variational mechanics with broad applicability to classical physical systems, is employed to formulate a novel attrition model for combat dynamics. This formulation extends the…
Learning the continuous dynamics of a system from snapshots of its temporal marginals is a problem which appears throughout natural sciences and machine learning, including in quantum systems, single-cell biological data, and generative…
We further develop a recently introduced variational principle of stationary action for problems in nonconservative classical mechanics and extend it to classical field theories. The variational calculus used is consistent with an initial…
In this article we provide a proof of the so called absolute continuity theorem for random dynamical systems on $R^d$ which have an invariant probability measure. First we present the construction of local stable manifolds in this case.…
It is shown that an oldest form of variational calculus of mechanics, the Maupertuis least action principle, can be used as a simple and powerful approach for the formulation of the variational principle for damped motions, allowing a…
Two ideas for the choice of an adequate set of coarse variables allowing approximate autonomous dynamics for practical applications are presented. The coarse variables are meant to represent averaged behavior of a fine-scale autonomous…
We introduce a variational algorithm, which solves the classical inverse Sturm-Liouville problem when two spectra are given. In contrast to other approaches, it recovers the potential as well as the boundary conditions without a priori…