Related papers: On Hamilton's Principle for Discrete and Continuou…

For any given spacetime the choice of time coordinate is undetermined. A particular choice is the absolute time associated with a preferred vector field. Using the absolute time Hamilton's equations are $- (\delta H_{c})/(\delta…

An exact invariant is derived for $n$-degree-of-freedom Hamiltonian systems with general time-dependent potentials. The invariant is worked out in two equivalent ways. In the first approach, we define a special {\it Ansatz\/} for the…

In this work, a kernel-based surrogate for integrating Hamiltonian dynamics that is symplectic by construction and tailored to large prediction horizons is proposed. The method learns a scalar potential whose gradient enters a…

This paper presents a "historical" formalism for dynamical systems, in its Hamiltonian version (Lagrangian version was presented in a previous paper). It is universal, in the sense that it applies equally well to time dynamics and to field…

A new method is proposed for integrating the equations of motion of an elastic filament. In the standard finite-difference and finite-element formulations the continuum equations of motion are discretized in space and time, but it is then…

The Hamiltonian approach to the General Relativity is formulated as a joint nonlinear realization of conformal and affine symmetries by means of the Dirac scalar dilaton and the Maurer-Cartan forms. The dominance of the Casimir vacuum…

I propose to use Hamiltonians which contain two-dimensional and three-dimensional kinetic terms for the description of two-dimensional systems in physics. As a model system the evolution of three-dimensional wavefunctions in the presence of…

We consider one-dimensional classical time-dependent Hamiltonian systems with quasi-periodic orbits. It is well-known that such systems possess an adiabatic invariant which coincides with the action variable of the Hamiltonian formalism. We…

When a set of particles are moving in a potential field, two aspects are concerned: 1) the relative motion of particle in spatial domain; 2) the particle velocity variations in time domain. The difficulty on treating the systems is…

Fractional generalization of an exterior derivative for calculus of variations is defined. The Hamilton and Lagrange approaches are considered. Fractional Hamilton and Euler-Lagrange equations are derived. Fractional equations of motion are…

It is shown that the well-known triviality of the Einstein field equations in two dimensions is not a sufficient condition for the Einstein-Hilbert action to be a total divergence, if the general covariance is to be preserved, that is, a…

Classical polarizable approaches have become the gold standard for simulating complex systems and processes in the condensed phase. These methods describe intrinsically dissipative polarizable media, requiring a formal definition within the…

Refined are the known descriptions of particle behavior with the help of Hamilton function in the phase space of coordinates and their multiple derivatives. This entails existing of circumstances when at closer distances gravitational…

We consider fluid flow across a permeable interface within a deformable porous medium. We use mixture theory. The mixture's constituents are assumed to be incompressible in their pure form. We use Hamilton's principle to obtain the…

We derive the dynamics of several rigid bodies of arbitrary shape in a 2-dimensional inviscid and incompressible fluid, whose vorticity field is given by point vortices. We adopt the idea of Vankerschaver et al. (2009) to derive the…

A general method to derive the diagonal representation for a generic matrix valued quantum Hamiltonian is proposed. In this approach new mathematical objects like non-commuting operators evolving with the Planck constant promoted as a…

The modal analysis is revisited through the symplectic formalism, what leads to two intertwined eigenproblems. Studying the properties of the solutions, we prove that they form a canonical basis. The method is general and works even if the…

We consider Hamiltonian formulation of a dynamical system forced to move on a submanifold $G_\alpha(q^A)=0$. If for some reasons we are interested in knowing the dynamics of all original variables $q^A(t)$, the most economical would be a…

The traditional method of teaching canonical transformations involves the introduction of generating functions of various types. This method obscures the underlying structure of the Hamiltonian least-action principle, and can make a…

In this paper we develop a fractional Hamiltonian formulation for dynamic systems defined in terms of fractional Caputo derivatives. Expressions for fractional canonical momenta and fractional canonical Hamiltonian are given, and a set of…