Related papers: An algebraic approach to systems with dynamical co…
We study the theory of systems with constraints from the point of view of the formal theory of partial differential equations. For finite-dimensional systems we show that the Dirac algorithm completes the equations of motion to an…
We describe the approximation of a continuous dynamical system on a p. l. manifold or Cantor set by a tractable system. A system is tractable when it has a finite number of chain components and, with respect to a given full background…
We review how an algebraic formulation for the dynamics of a physical system allows to describe a reduction procedure for both classical and quantum evolutions.
Constrained quantum dynamics is used to propose a nonlinear dynamical equation for pure states of a generalized coarse-grained system. The relevant constraint is given either by the generalized purity or by the generalized invariant…
It is shown that introducing the quantum effects using deBroglie--Bohm theory in the canonical formulation of gravity would change the constraints algebra. The new algebra is derived and shown that it is the clear projection of general…
The time dependent-integrals of motion, linear in position and momentum operators, of a quantum system are extracted from Noether's theorem prescription by means of special time-dependent variations of coordinates. For the stationary case…
Newtonian dynamical systems which accept the normal shift on an arbitrary Riemannian manifold are considered. For them the determinating equations making the weak normality condition are derived. The expansion for the algebra of tensor…
A geometric approach to integrability and reduction of dynamical system is developed from a modern perspective. The main ingredients in such analysis are the infinitesimal symmetries and the tensor fields that are invariant under the given…
We introduce a model of infinite horizon linear dynamic optimization with linear constraints and obtain results concerning feasibility of trajectories and optimal solutions necessarily satisfying conditions that resemble the Euler condition…
In this paper we have obtained some dynamics equations, in the presence of nonlinear nonholonomic constraints and according to a lagrangian and some Chetaev-like conditions. Using some natural regular conditions, a simple form of these…
We study the nonlinear realization of supersymmetry in a dynamical/cosmological background in which derivative terms like kinetic terms are finite. Starting from linearly realized theories, we integrate out heavy modes without neglecting…
Invariance theorems in analytical mechanics, such as Noether's theorem, can be adapted to continuum mechanics. For this purpose, it is useful to give a functional representation of the motion and to interpret the groups of invariance with…
An effective mathematical framework based on Presymplectic Geometry for dealing with the "phase space picture" of timeless dynamics in General Relativity is presented. In General Relativity, the presence of the scalar Hamiltonian constraint…
We present new approaches for solving constrained multicomponent nonlinear Schr\"odinger equations in arbitrary dimensions. The idea is to introduce an artificial time and solve an extended damped second order dynamic system whose…
Linear systems under the influence of nonlinear and random linear perturbations, and with random initial and boundary conditions, are discussed. The notion of states of a system is substituted by the notion of the generating vectors for…
In the framework of the generalized Hamiltonian formalism by Dirac, the local symmetries of dynamical systems with first- and second-class constraints are investigated in the general case without restrictions on the algebra of constraints.…
An application design is offered, which students of physics can use when authoring a solver for mechanical systems with constraints. A 'chainlist' concept is introduced to capture a constrained mechanical system configuration and to pass…
We explore how to build a vector field from the various functions involved in a given mathematical program, and show that locally-stable equilibria of the underlying dynamical system are precisely the local solutions of the optimization…
In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this part we consider orbital motion in transverse plane for a single…
In the history of mechanics, there have been two points of view for studying mechanical systems: Newtonian and Cartesian. According the Descartes point of view, the motion of mechanical systems is described by the first-order differential…