Related papers: Energy and Angular Momentum Dependent Potentials w…
After some more than four centuries from the formulation and publication (in Astronomia Nova) of the Kepler's Equation, which relates the eccentric (and, intermediately, the true) anomaly of the planetary trajectories to the uniformly…
A pure two-body problem has seven integrals including the Kepler energy, the Laplace vector, and the angular momentum vector. However, only five of them are independent. When the five independent integrals are preserved, the two other…
The equation for the conic sections describing the possible orbits in a potential $V \sim r^{-1}$ is obtained by means of a vector constant of the motion differing from the traditional Laplace-Runge-Lenz vector.
An explicitly orbital-dependent correlation energy functional is proposed, which is to be used in combination with the orbital-dependent exchange energy functional in energy-band calculations. It bears a close resemblance to the…
Using Euler's equations of motion and the Hamiltonian formulation, we obtain the equations of motion of systems with internal angular momentum that are moving with respect to a given reference frame, when subjected to a torque which is…
A new formulation is presented for a variational calculation of $N$-body systems on a correlated Gaussian basis with arbitrary angular momenta. The rotational motion of the system is described with a single spherical harmonic of the total…
A discrete and exact algorithm for obtaining planetary systems is derived in a recent article (Eur. Phys. J. Plus 2022, 137:99). Here the algorithm is used to obtain planetary systems with forces different from the Newtonian inverse square…
We study the dynamics of two bodies moving on elliptic Keplerian orbits around a fixed center of attraction and interacting only by means of elastic or inelastic collisions. We show that there exists a bounded invariant region: for suitable…
In this paper we present both the classical and quantum periodic-orbits of a neutral spinning particle constrained in two-dimensional central-potentials with a cylindrically symmetric electric-field in addition which leads to an effective…
A new variational principle - extremizing the fixed frame kinetic energy under constant relative enstrophy - for a coupled barotropic flow - rotating solid sphere system is introduced with the following consequences. In particular, angular…
We will show that the period $T$ of a closed orbit of the planar circular restricted three-body problem (viewed on rotating coordinates) depends on the region it encloses. Roughly speaking, we show that, $2 T=k\pi+\int_\Omega g$ where $k$…
The increasing number and variety of extrasolar planets illustrates the importance of characterizing planetary perturbations. Planetary orbits are typically described by physically intuitive orbital elements. Here, we explicitly express the…
We argue that in the general relativistic calculation of planetary orbits, the choice of a reference frame which is an obligatory condition in the Newtonian approach is replaced by an appropriate boundary condition on the solution of…
Ring geometries have fascinated experimental and theoretical physicists over many years. Open rings connected to leads allow the observation of the Aharonov-Bohm effect, a paradigm of quantum mechanical phase coherence. The phase coherence…
We consider the Newtonian 3-body problem in dimension 4, and fix a value of the angular momentum which is compatible with this dimension. We show that the energy function cannot tend to its infimum on an unbounded sequence of states.…
The violation of local uncertainty relations is a valuable tool for detecting entanglement, especially in multi-dimensional systems. The orbital angular momentum of light provides such a multi-dimensional system. We study quantum…
Using a quantum fluid model, a set of three paraxial coupled equations to describe the FEL instability is derived. These equations are solved numerically considering Laguerre-Gaussian modes as the initial conditions to study the transfer of…
In this article we develop in detail a causal model of the hydrogen atom, building on the earlier work of Dewdney and Malik [1] in which they outlined a causal model of the hydrogen atom, focusing more on a causal model of angular momentum…
This paper revisits earlier work on complex classical mechanics in which it was argued that when the energy of a classical particle in an analytic potential is real, the particle trajectories are closed and periodic, but that when the…
The validity of the orbital motion limited (OML) theory is reviewed with reference to the floating potential acquired by a spherical object immersed in a plasma. A new and perhaps more realistic approach for obtaining the floating potential…