相关论文: Holonomic constraints : an analytical result

We provide a correction to the sufficient conditions under which closed-form expressions for the optimal Lagrange multiplier are provided in arXiv:2112.13138 [math.OC]. We first present a simple counterexample where the original conditions…

We deal with regular Lagrangian constrained systems which are invariant under the action of a symmetry group. Fixing a connection on the higher-order principal bundle where the Lagrangian and the (independent) constraints are defined, the…

We propose a method of quantization based on Hamilton-Jacobi theory in the presence of a random constraint due to the fluctuations of a set of hidden random variables. Given a Lagrangian, it reproduces the results of canonical quantization…

The gauge symmetries of a general dynamical system can be systematically obtained following either a Hamiltonean or a Lagrangean approach. In the former case, these symmetries are generated, according to Dirac's conjecture, by the first…

Compressed Sensing (CS) encompasses a broad array of theoretical and applied techniques for recovering signals, given partial knowledge of their coefficients. Its applications span various fields, including mathematics, physics,…

An extension of Riewe's fractional Hamiltonian formulation is presented for fractional constrained systems. The conditions of consistency of the set of constraints with equations of motion are investigated. Three examples of fractional…

In this paper, we propose a second-order energy-conserving approximation procedure for Hamiltonian systems with holonomic constraints. The derivation of the procedure relies on the use of the so-called line integral framework. We provide…

This paper presents a formulation of Lagrangian dynamics of constrained mechanical systems in terms of reduced quasi-velocities and quasi-forces that can be used for simulation, analysis, and control purposes. In this formulation, Cholesky…

The main theme of the article is the study of discrete systems of material points subjected to constraints not only of a geometric type (holonomic constraints) but also of a kinematic type (nonholonomic constraints). The setting up of the…

In this study, it is generalized the concept of Lagrangian mechanics with constraints to complex case. To be beginning, it is considered a Kaehlerian manifold as a velocity-phase space. Then a non-holonomic constraint is given by 1-form on…

A formalism for the study of highly interacting electronic systems is presented. The proposed scheme is based on two key concepts: composite operators and algebra constraints. Composite field operators, that naturally appear as a…

We derive the Hamilton equations of motion for a constrained system in the form given by Dirac, by a limiting procedure, starting from the Lagrangean for an unconstrained system. We thereby ellucidate the role played by the primary…

Multiplicity results for solutions of various boundary value problems are known for dynamical systems on compact configuration manifolds, given by Lagrangians or Hamiltonians which have quadratic growth in the velocities or in the momenta.…

In this note, three Lagrange multiplier rules introduced in the literature for set valued optimization problems are compared. A generalization of all three results is given which proves that under rather mild assumptions, $x$ is a weak…

This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…

In a space of 4-dimensions, I will examine constrained variational problems in which the Lagrangian, and constraint scalar density, are concomitants of a (pseudo-Riemannian) metric tensor and its first two derivatives. The Lagrange…

We construct an operational formulation of classical mechanics without presupposing previous results from analytical mechanics. In doing so, several concepts from analytical mechanics will be rediscovered from an entirely new perspective.…

Constraints imposed directly on accelerations of the system leading to the relation of constants of motion with appropriate local projectors occurring in the derived equations are considered. In this way a generalization of the Noether's…

Holographic algorithms introduced by Valiant are composed of two ingredients: matchgates, which are gadgets realizing local constraint functions by weighted planar perfect matchings, and holographic reductions, which show equivalences among…

Critical points of a function subject to a constraint can be either detected by restricting the function to the constraint or by looking for critical points of the Lagrange multiplier functional. Although the critical points of the two…