Related papers: Non-holonomic Constraint Force Postulates

The canonical formalism of the (2+2) formulation of general relativity of 4 spacetime dimensions is studied under no symmetry assumptions, where the spacetime is viewed as a local product of a 2 dimensional base manifold of Lorentzian…

The Hamiltonian theory of a relativistic string is considered in a specific reference frame in terms the diffeo-invariant variables. The evolution parameter and energy invariant with respect to the time-coordinate transformations are…

In this paper we use an affine connection formulation to study an optimal control problem for a class of nonholonomic, under-actuated mechanical systems. In particular, we aim at minimizing the norm-squared of the control input to move the…

This short note is devoted to the canonical analysis of the non-local theories of gravity. We find their Hamiltonian and determine the algebra of constraints. We perform this analysis for non-local theories of gravity formulated both in…

Lagrangian systems with nonholonomic constraints may be considered as singular differential equations defined by some constraints and some multipliers. The geometry, solutions, symmetries and constants of motion of such equations are…

Dynamical systems, described by Lagrangians with first- and second-class constraints, are investigated. In the Dirac approach to the generalized Hamiltonian formalism, the classification and separation of the first- and second-class…

Nonholonomic systems are, so to speak, mechanical systems with a prescribed restriction on the velocities. A virtual nonholonomic constraint is a controlled invariant distribution associated with an affine connection mechanical control…

Standandard Hamiltonian mechanics in its homogeneous formulation is applied to the study of discontinuities representing rapid changes of Hamiltonians. Different formulations of Hamiltonian mechanics are reviewed. An original representation…

Hamiltonian Monte Carlo has emerged as a standard tool for posterior computation. In this article, we present an extension that can efficiently explore target distributions with discontinuous densities. Our extension in particular enables…

A diagonal version of the strong reflection principle is introduced, along with fragments of this principle associated to arbitrary forcing classes. The relationships between the resulting principles and related principles, such as the…

We give a partial review of what is known so far on stability of periodically driven quantum systems versus regularity of the bounded driven force. In particular we emphasize the fact that unbounded degeneracies of the unperturbed…

For a Lagrangian system with nonholonomic constraints, we construct extensions of the equations of motion to sets of second-order ordinary differential equations. In the case of a purely kinetic Lagrangian, we investigate the conditions…

This paper deals with an improvement of the "a-priori stability bounds" on the variation of the action variables and on the stability time obtained from a given Birkhoff normal form around the elliptic equilibrium point of an Hamiltonian…

Necessary conditions for existence of normal extremals in optimal control of systems subject to nonholonomic constraints are derived as solutions of a constrained second order variational problems. In this work, a geometric interpretation…

The non-emptiness, called the Domino Problem, and the characterization of the possible entropies of $\mathbb{Z}^2$-subshifts of finite type are standard problems of symbolic dynamics. In this article we study these questions with horizontal…

The main aim of the present paper is to raise the doubt that vakonomic dynamics may not be satisfactory as a model for velocity dependent constraints.

Equilibrium statistics of Hamiltonian systems is correctly described by the microcanonical ensemble, whereas canonical ones fail in the most interesting, mostly inhomogeneous, situations like phase separations or away from the thermodynamic…

We consider quantum mechanics on constrained surfaces which have non-Euclidean metrics and variable Gaussian curvature. The old controversy about the ambiguities involving terms in the Hamiltonian of order hbar^2 multiplying the Gaussian…

Conditions for the validity of the quantum adiabatic approximation are analyzed. For the case of linear Hamiltonians, a simple and general sufficient condition is derived, which is valid for arbitrary spectra and any kind of time variation.…

Using dimensional analysis techniques we present an extension of Newton's gravitational theory built under the assumption that Milgrom's acceleration constant is a fundamental quantity of nature. The gravitational force converges to…