相关论文: On Virtual Displacement and Virtual Work in Lagran…

In the context of Faraday's induction law, we show that the concept of virtual work provides another point of view to clarify the nature of the induced electric field, as well as the fact that the integral over a closed path of the induced…

We introduce the concept of a "transitory" dynamical system---one whose time-dependence is confined to a compact interval---and show how to quantify transport between two-dimensional Lagrangian coherent structures for the Hamiltonian case.…

The application of the Legendre transformation to a hyperregular Lagrangian system results in a Hamiltonian vector field generated by a Hamiltonian defined on the phase space of the mechanical system. The Legendre transformation in its…

We present a direct approach to the construction of Lagrangians for a large class of one-dimensional dynamical systems with a simple dependence (monomial or polynomial) on the velocity. We rederive and generalize some recent results and…

For integrable systems in the sense of multidimensional consistency (MDC) we can consider the Lagrangian as a form, which is closed on solutions of the equations of motion. For 2-dimensional systems, described by partial difference…

A system with anholonomic constraints where the trajectories of physical degrees of freedom are autoparallels on a manifold equipped with a general Cartan connection is discussed. A variational principle for the autoparallel trajectories is…

If the uncertainty principle applies to the Verlinde entropic idea, it leads to a new term in the Newton's second law of mechanics in the Planck's scale. This curious velocity dependence term inspires a frictional feature of the gravity. In…

Serious mathematical defect in the important kinematics theorem known in continuum mechanics as Convection (or Transport) Theorem is reported. We claim that the traditional demonstration does not take into account a special constraint on…

Systems subjected to holonomic constraints follow quite complicated dynamics that could not be described easily with Hamiltonian or Lagrangian dynamics. The influence of holonomic constraints in equations of motions is taken into account by…

The principle of virtual power is used to derive the equilibrium field equations of a porous solid saturated with a fluid, including second density-gradient effects; the intention is the elucidation and extension of the effective stress…

In this paper, we address the problem of stabilizing a system around a desired manifold determined by virtual nonlinear nonholonomic constraints. Virtual constraints are relationships imposed on a control system that are rendered invariant…

The problem of rigid body pose estimation is treated in discrete-time via discrete Lagrange-d'Alembert principle and discrete Lyapunov methods. The position and attitude of the rigid body are to be estimated simultaneously with the help of…

Visual navigation typically assumes the existence of at least one obstacle-free path between start and goal, which must be discovered/planned by the robot. However, in real-world scenarios, such as home environments and warehouses, clutter…

We consider parallel simulations for asynchronous systems employing L processing elements that are arranged on a ring. Processors communicate only among the nearest neighbors and advance their local simulated time only if it is guaranteed…

Previous work in the literature has studied the Hamiltonian structure of an R-squared model of gravity with torsion in a closed Friedmann-Robertson-Walker universe. Within the framework of Dirac's theory, torsion is found to lead to a…

Five-vectors theory of gravity is proposed, which admits an arbitrary choice of the energy density reference level. This theory is formulated as the constraint theory, where the Lagrange multipliers turn out to be restricted to some class…

In spite of its long history and classical character which goes back even to d'Alembert and Lagrange, the problems of constraints in mechanics of continua is still mysterious and full of misunderstandings. Let us mention the problem of…

There are many different formulations of relativistic elasticity. Most of them are only concerned with formal questions rather than questions regarding the PDE point of view. The aim of this thesis is to obtain various local existence…

We first present a way to formulate the equations of motion for a nonholonomic system with nonlinear constraints with respect to the velocities. The formulation is based on the Cetaev condition which aims to extend the practical method of…

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…