Related papers: Comment on a theorem of Hamilton
We consider a classical spinning particle in the frame of the relativistic physics by means of a covariant Hamiltonian and of a generalization of Poisson brackets which take into account the gauge fields. We obtain different equations of…
The algebra of the relativistic composition of velocities is shown to be isomorphic to an algebraic loop defined on division algebras. This makes calculations in special relativity effortless and straightforward, unlike the standard…
For a finite set $S$ of points in the plane and a graph with vertices on $S$ consider the disks with diameters induced by the edges. We show that for any odd set $S$ there exists a Hamiltonian cycle for which these disks share a point, and…
Suppose that $H(q,p)$ is a Hamiltonian on a manifold $M$, and $\tilde L(q,\dot q)$, the Rayleigh dissipation function, satisfies the same hypotheses as a Lagrangian on the manifold $M$. We provide a Hamiltonian framework that gives the…
A new proof of the geodesic character of all motions of bodies that interact only gravitationally - and a detailed illustration of the real meaning of the linearized approximation of general relativity.
Given a constant of motion for the one-dimensional harmonic oscillator with linear dissipation in the velocity, the problem to get the Hamiltonian for this system is pointed out, and the quantization up to second order in the perturbation…
An earlier paper [1] presented a gravity theory based on the optics of de Broglie waves rather than curved space-time. While the universe's geometry is flat, it agrees with the standard tests of general relativity. A second paper [2] showed…
It is shown that change in transverse momentum of a relativistic particle, crossing an accelerating cavity parallel to its axis, may be presented as an integral over trajectory, the integrand of which is proportional to the component of…
This paper gives a technically elementary treatment of some aspects of Hamilton-Jacobi theory, especially in relation to the calculus of variations. The second half of the paper describes the application to geometric optics, the…
We give a straightforward and divergence free derivation of the equation of motion for a small but finite object in an arbitrary background using strong field point particle limit. The resulting equation becomes a generalized geodesic for a…
A generalization of the Dirac's canonical quantization theory for a system with second-class constraints is proposed as the fundamental commutation relations that are constituted by all commutators between positions, momenta and Hamiltonian…
The complete variables separation is given for one Hamiltonian system with two degrees of freedom arising in the motion of the Kowalevski type top in two constant fields.
A vacuum medium model is advanced. The motion of a relativistic particle in relation to its interaction with the medium is discussed. It is predicted that elementary excitations of the vacuum, called "inertons," should exist. The equations…
We suggest the Hamiltonian approach for fluid mechanics based on the dynamics, formulated in terms of Lagrangian variables. The construction of the canonical variables of the fluid sheds a light of the origin of Clebsh variables, introduced…
In our previous papers [11,13] we showed that the Hamilton-Jacobi problem can be regarded as a way to describe a given dynamics on a phase space manifold in terms of a family of dynamics on a lower-dimensional manifold. We also showed how…
The spontaneous motion of a camphor particle with a slight modification from a circle is investigated. The effect of the shape on the motion is examined by the perturbation method. We introduce a slight $n$-mode modification from a circle,…
We compute the normal forms for the Hamiltonian leading to the epicyclic approximations of the (perturbed) Kepler problem in the plane. The Hamiltonian setting corresponds to the dynamics in the Hill synodic system where, by means of the…
In the relativistic uniform model for continuous medium the integral theorem of generalized virial is derived, in which generalized momenta are used as particles momenta. This allows us to find exact formulas for the radial component of the…
It is shown that if a non-autonomous system of $2n$ first-order ordinary differential equations is expressed in the form of the Hamilton equations in terms of two different sets of coordinates, $(q_{i}, p_{i})$ and $(Q_{i}, P_{i})$, then…
We give a proof of the KAM theorem on the existence of invariant tori for weakly perturbed Hamiltonian systems, based on Thirring's approach for Hamiltonians that are quadratic in the action variables. The main point of this approach is…