Related papers: Transpositional rule for constrained systems
A nonholonomic system consists of a configuration space Q, a Lagrangian L, and an nonintegrable constraint distribution H, with dynamics governed by Lagrange-d'Alembert's principle. We present two studies both using adapted moving frames.…
We have recently presented an extension of the standard variational calculus to include the presence of deformed derivatives in the Lagrangian of a system of particles and in the Lagrangian density of field-theoretic models. Classical…
Hamilton's principle is extended to have compatible initial conditions to the strong form. To use a number of computational and theoretical benefits for dynamical systems, the mixed variational formulation is preferred in the systems other…
The continuum equations of fluid mechanics are rederived with the intention of keeping certain mechanical and thermodynamic concepts separate. A new "mechanical" mass density is created to be used in computing inertial quantities, whereas…
The reasons which restrict opportunities of classical mechanics at the description of nonequilibrium systems are discussed. The way of overcoming of the key restrictions is offered. This way is based on an opportunity of representation of…
The recent work, Nemoto and Sasa [Phys. Rev. E, 83: 030105(R) (2011)], has shown that large deviations of the current characterizing a nonequilibrium system are obtained by observing the typical current for a modified system specified by a…
In this article we study virtual nonholonomic constraints, which are relations between the generalized coordinates and momenta of a mechanical system that can be enforced via feedback control. We design a constraint which emulates…
The Hamilton principle is a variation principle describing the isolated and conservative systems, its Lagrange function is the difference between kinetic energy and potential energy. By Feynman path integration, we can obtain the Hermitian…
This paper presents a geometric description of Lagrangian and Hamiltonian systems on Lie affgebroids subject to affine nonholonomic constraints. We define the notion of nonholonomically constrained system, and characterize regularity…
We derive the equations of nonlinear magnetoelastostatics using several variational formulations involving the mechanical deformation and an independent field representing the magnetic component. An equivalence is also discussed, modulo…
The aim of this paper is to study a wide class of non-convex sweeping processes with moving constraint whose translation and deformation are represented by regulated functions, i.e., functions of not necessarily bounded variation admitting…
Hamilton variational principle for special type of statistical ensemble of deterministic dynamical systems is derived. Thie form of variational principle allows one to describe the statistical ensemble in terms of wave functions and…
Variational formulations of statics and dynamics of mechanical systems controlled by external forces are presented as examples of variational principles.
Extremal principles can generally be divided into two rather distinct classes. There are, on the one hand side, formulations based on the Lagrangian or Hamiltonian mechanics, respectively, dealing with time dependent problems, but…
It is proposed how to impose a general type of ''noncommutativity'' within classical mechanics from first principles. Formulation is performed in completely alternative way, i.e. without any resort to fuzzy and/or star product philosophy,…
An extension of the Legendre transform to non-convex functions with vanishing Hessian as a mix of envelope and general solutions of the Clairaut equation is proposed. Applying this to systems with constraints, the procedure of finding a…
Some problems on variations are raised for classical discrete mechanics and field theory and the difference variational approach with variable step-length is proposed motivated by Lee's approach to discrete mechanics and the difference…
We propose an extension of the classical variational theory of evolution equations that accounts for dynamics also in possibly non-reflexive and non-separable spaces. The pivoting point is to establish a novel variational structure, based…
The interplay between off-shell and on-shell unfolded systems is analysed. The formulation of invariant constraints that put an off-shell system on shell is developed by adding new variables and derivation in the target space, that extends…
The purpose of this paper is to show that, at least for Lagrangians of mechanical type, nonholonomic Euler-Lagrange equations for a nonholonomic linear constraint D may be viewed as non-constrained Euler-Lagrange equations but on a new…