Related papers: The Least Action-Augmented Lanchester Model
We introduce a minimization formulation for the determination of a finite-dimensional, time-dependent, orthonormal basis that captures directions of the phase space associated with transient instabilities. While these instabilities have…
In this paper we develop a general conceptual approach to the problem of existence of action-angle variables for dynamical systems, which establishes and uses the fundamental conservation property of associated torus actions: anything which…
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…
We develop an information-theoretic formulation of stochastic dynamics in which the fundamental stochastic variable is the total action connecting spacetime points, rather than individual paths. By maximizing Shannon entropy over a joint…
We address a degenerate elliptic variational problem arising in the application of the least action principle to averaged solutions of the inhomogeneous Euler equations in Boussinesq approximation emanating from the horizontally flat…
The "ratchet principle" asserts that non-equilibrium systems which violate parity symmetry generically exhibit steady-state currents. As recently shown, there are exceptions to this principle, due to the existence of hidden time-reversal…
Employing a phase space which includes the (Riemann-Liouville) fractional derivative of curves evolving on real space, we develop a restricted variational principle for Lagrangian systems yielding the so-called restricted fractional…
The Homotopy Analysis Method (HAM) is a powerful technique which allows to derive approximate solutions of both ordinary and partial differential equations. We propose to use a variational approach based on the Least Action Principle (LAP)…
We consider the problem of constructing an action functional for physical systems whose classical equations of motion cannot be directly identified with Euler-Lagrange equations for an action principle. Two ways of action principle…
A discrete action principle for general quantum automata is proposed. This action principle is particularized to Discrete Time Quantum Walks (DTQWs) and then extended into an energy and momentum preserving, manifestly covariant formulation.…
This contribution aims to shed light on mathematical epidemic dynamics modelling from the viewpoint of analytical mechanics. To set the stage, it recasts the basic SIR model of mathematical epidemic dynamics in an analytical mechanics…
The variational principle for a spherical configuration consisting of a thin spherical dust shell in gravitational field is constructed. The principle is consistent with the boundary-value problem of the corresponding Euler-Lagrange…
Identifying physical laws from noisy observational data is a central challenge in scientific machine learning. We present Minimum-Action Learning (MAL), a framework that selects symbolic force laws from a pre-specified basis library by…
The outcomes of warfare have rarely only been characterised by the quantity and quality of individual combatant force elements. The ability to manoeuvre and adapt across force elements through effective Command and Control (C2) can allow…
In spirit of the principle of least action, which means that when a perturbation is applied to a physical system its reaction is such that it modifies its state to "agree" with the perturbation by "minimal" change of its initial state. In…
In physics, there is a scalar function called the action which behaves like a cost function. When minimized, it yields the "path of least action" which represents the path a physical system will take through space and time. This function is…
Motivated by robotic trajectory optimization problems we consider the Augmented Lagrangian approach to constrained optimization. We first propose an alternative augmentation of the Lagrangian to handle the inequality case (not based on…
In this report the authors examine the possibility of using the Fractal Attrition Equation as a metamodel to describe outcomes of cellular automaton combat models. This Fractal Attrition Equation has been proposed as a replacement for the…
In the paper a simple discrete dynamical model for dynamics of two antagonistic agents (opponents) under iterated sanctions and counter-sanctions is proposed. The model is inspired with Osipov-Lanchester model for combats. Simple stability…
We introduce a minimal model consisting of a two-body system with stochastically broken reciprocity (i.e., random violation of Newton's third law) and then investigate its statistical behaviors, including fluctuations of velocity and…