Related papers: Understanding the Hamiltonian Function through the…

The standard Hamiltonian machinery, being applied to field theory, leads to infinite-dimensional phase spaces. It is not covariant. In this article, we present covariant finite-dimensional multimomentum Hamiltonian formalism for field…

All measurable predictions of classical mechanics can be reproduced from a quantum-like interpretation of a nonlinear Schrodinger equation. The key observation leading to classical physics is the fact that a wave function that satisfies a…

Non-standard Lagrangians do not display any discernible energy-like terms, yet they give the same equations of motion as standard Lagrangians, which have easily identifiable energy-like terms. A new method to derive non-standard Lagrangians…

Hamiltonian mechanics is an effective tool to represent many physical processes with concise yet well-generalized mathematical expressions. A well-modeled Hamiltonian makes it easy for researchers to analyze and forecast many related…

In this paper we consider a generalized classical mechanics with fractional derivatives. The generalization is based on the time-clock randomization of momenta and coordinates taken from the conventional phase space. The fractional…

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…

We extend some aspects of the Hamilton-Jacobi theory to the category of stochastic Hamiltonian dynamical systems. More specifically, we show that the stochastic action satisfies the Hamilton-Jacobi equation when, as in the classical…

A short review of basic formulas from Hamiltonian formalism in classical mechanics in the case when Lagrangian contains N time-derivatives of n coordinate variables. For non-local models N=infinity.

The question posed in the title is answered in terms of a simple pictorial argument that is manifestly symmetric between the two functions that are Legendre transform of each other.

The construction of effective Lagrangians commonly involves the application of the `classical equation of motion' to eliminate redundant structures and thus generate the minimal number of independent terms. We investigate this procedure in…

Within the frames of the analytical mechanics the method of the description of dynamics of nonequilibrium systems of potentially interacting elements is develops. The method is based on an opportunity of representation of nonequilibrium…

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…

It is widely accepted that the fundamental geometrical law of nature should follow from an action principle. The particular subset of transformations of a system's dynamical variables that maintain the form of the action principle comprises…

Through duality it is possible to transform left fractional operators into right fractional operators and vice versa. In contrast to existing literature, we establish integration by parts formulas that exclusively involve either left or…

I show how Hamilton's philosophical commitments led him to a causal interpretation of classical mechanics. I argue that Hamilton's metaphysics of causation was injected into his dynamics by way of a causal interpretation of force. I then…

Novel gauge functions are introduced to non-relativistic classical mechanics and used to define forces. The obtained results show that the gauge functions directly affect the energy function and that they allow converting an undriven…

The variational formulation for Lie-transform Hamiltonian perturbation theory is presented in terms of an action functional defined on a two-dimensional parameter space. A fundamental equation in Hamiltonian perturbation theory is shown to…

The Lagrangian formalism is developed for the population dynamics of interacting species that are described by several well-known models. The formalism is based on standard Lagrangians, which represent differences between the physical…

We study the constrained Ostrogradski-Hamilton framework for the equations of motion provided by mechanical systems described by second-order derivative actions with a linear dependence in the accelerations. We stress out the peculiar…

The main purpose in the present paper is to build a Hamiltonian theory for fields which is consistent with the principles of relativity. For this we consider detailed geometric pictures of Lepage theories in the spirit of Dedecker and try…