Related papers: Constrained ballistics and geometrical optics
Finite dimensional models that mimic the constraint structure of Einstein's General Relativity are quantized in the framework of BRST and Dirac's canonical formalisms. The first system to be studied is one featuring a constraint quadratic…
We study a class of nonlinear nonparametric inverse problems. Specifically, we propose a nonparametric estimator of the dynamics of a monotonically increasing trajectory defined on a finite time interval. Under suitable regularity…
In this work, we investigate a Lagrangian model describing a particle constrained to move along non-degenerate conic sections, parameterized by the orbital eccentricity \( e \). In the non-relativistic regime, we apply the Dirac--Bergmann…
We examine the transformation of particle trajectories in models with deformations of Special Relativity that have an energy-dependent and observer-independent speed of light. These transformations necessarily imply that the notion of what…
The minimum-time path for intercepting a moving target with a prescribed impact angle is studied in the paper. The candidate paths from Pontryagin's maximum principle are analyzed, so that each candidate is related to a zero of a…
In this paper we are interested in a new type of {\it mean-field}, non-Markovian stochastic control problems with partial observations. More precisely, we assume that the coefficients of the controlled dynamics depend not only on the paths…
Recently, there has been an increasing interest in modelling and computation of physical systems with neural networks. Hamiltonian systems are an elegant and compact formalism in classical mechanics, where the dynamics is fully determined…
In this paper, we present a detailed review/analysis of the Dirac quantisation of Hamiltonian systems with constraints. To this end, we use, as a guide, the physical example provided by the dynamics of a solid ball rolling, without…
A formulation of singular classical theories (determined by degenerate Lagrangians) without constraints is presented. A partial Hamiltonian formalism in the phase space having an initially arbitrary number of momenta (which can be smaller…
Although there is no relative motion among different points on a rotating disc, each point belongs to a different noninertial frame. This fact, not recognized in previous approaches to the Ehrenfest paradox and related problems, is…
The Floydian trajectory method of quantum mechanics and the appearance of microstates of the Schr\"{o}dinger equation are reviewed and contrasted with the Bohm interpretation of quantum mechanics. The kinematic equation of Floydian…
An optimal control problem for longitudinal motions of a thin elastic rod is considered. We suppose that a normal force, which changes piecewise constantly along the rod's length, is applied to the cross-section so that the positions of…
A number of optimization algorithms have been inspired by the physics of Newtonian motion. Here, we ask the question: do algorithms themselves obey some ``natural laws of motion,'' and can they be derived by an application of these laws? We…
Stochastic contraction analysis is a recently developed tool for studying the global stability properties of nonlinear stochastic systems, based on a differential analysis of convergence in an appropriate metric. To date, stochastic…
We develop a rigorous framework for global non-convex optimization by reformulating the minimization problem as a discounted infinite-horizon optimal control problem. For non-convex, continuous, and possibly non-smooth objective functions…
We focus on the solutions of second-order stable linear difference equations and demonstrate that their behavior can be non-monotone and exhibit peak effects depending on initial conditions. The results are applied to the analysis of the…
We consider the tracking of geometric paths in output spaces of nonlinear systems subject to input and state constraints without pre-specified timing requirements. Such problems are commonly referred to as constrained output path-following…
The maximum surveillance of a target which is holding course is considered, wherein an observer vehicle aims to maximize the time that a faster target remains within a fixed-range of the observer. This entails two coupled phases: an…
The Hamiltonian description for a wide class of mechanical systems, having local symmetry transformations depending on time derivatives of the gauge parameters of arbitrary order, is constructed. The Poisson brackets of the Hamiltonian and…
This work is concerned with optimal control of partial differential equations where the control enters the state equation as a coefficient and should take on values only from a given discrete set of values corresponding to available…