相关论文: Nonholonomic constrains: why does not the least ac…
Following the formalism of Gell-Mann and Hartle, phenomenological equations of motion are derived from the decoherence functional formalism of quantum mechanics, using a path-integral description. This is done explicitly for the case of a…
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.…
We consider the problem of a conditional extremum of an action in a class of fields constrained by differential equations. For this setup, we propose an extension of Noether's first theorem to connect the symmetries of the action and the…
One of the earliest formulations of dynamics of nonholonomic systems traces back to 1895 and it is due to Caplygin, who developed his analysis under the assumption that a certain number of the generalized coordinates do not occur neither in…
The action principle is introduced to describe the thermodynamic processes of the state functions from the initial equilibrium state to the final equilibrium state. To capture the path-independent property of the state functions through the…
The Principle of Least Action is used with a simple Lagrangian density, involving second-order derivatives of the wave function, to obtain the Schroedinger equation. A Hamiltonian density obtained from this simple Lagrangian density shows…
A general prescription for the treatment of constrained quantum motion is outlined. We consider in particular constraints defined by algebraic submanifolds of the quantum state space. The resulting formalism is applied to obtain solutions…
The derivation of the recently proposed nonlinear quantum evolution of gravity from an action principle is considered in this brief note. It is shown to be possible if a set of consistency conditions are satisfied that are analogous to the…
We present an action principle formulation for the study of motion of an extended body in General Relativity in the limit of weak gravitational field. This gives the classical equations of motion for multipole moments of arbitrary order…
Mechanics can be founded in a principle stating the uncertainty in the position of an observable particle delta-q as a function of its motion relative to the observer, expressed in a trajectory representation . From this principle,…
Nonholonomic mechanics describes the motion of systems constrained by nonintegrable constraints. One of its most remarkable properties is that the derivation of the nonholonomic equations is not variational in nature. {However, in} this…
A new approach to relativistic mechanics is proposed, suitable to describe dynamics of different kinds of relativistic particles. Mathematically it is based on an application of the recent geometric theory of nonholonomic systems on fibred…
The Hamilton action principle, also known as the principle of least action, and Lagrange equations are an integral part of advanced undergraduate mechanics. At present, substantial efforts are ongoing to suitably incorporate the action…
We propose a first example of a simple classical field theory with nonholonomic constraints. Our model is a straightforward modification of a Cosserat rod. Based on a mechanical analogy, we argue that the constraint forces should be modeled…
If evolution can be connected to the principle of least action, and if it is depicted in evolution space versus time then it corresponds to the direction of ultimate causation. As an organism evolves and follows a path of proximate…
Quantum correlations and other phenomena characteristic to a quantum world can be understood as simply consequences of a principle derived from the postulates of Quantum Mechanics. This explanatory principle states that these phenomena…
Cracks in beams and shallow arches are modeled by massless rotational springs. First, we introduce a specially designed linear operator that "absorbs" the boundary conditions at the cracks. Then the equations of motion are derived from the…
Hardly any real self-propelling or actively driven object is perfect. Thus, undisturbed motion will generally not follow straight lines but rather circular trajectories. We here address self-propelled or actively driven objects that move in…
It is shown that for a relativistic particle moving in an electromagnetic field its equations of motion written in a form of the second law of Newton can be reduced with the help of elementary operations to the Hamilton-Jacobi equation. The…
Chemical affinities are responsible for driving active matter systems out of equilibrium. At the nano-scale, molecular machines interact with the surrounding environment and are subjected to external forces. The mechano-chemical coupling…