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We present a novel numerical method to calculate periodic orbits for dynamical systems by an iterative process which is based directly on the action integral in classical mechanics. New solutions are obtained for the planar motion of three…
Charged fluids rotating around compact objects can form unique equilibrium structures when ambient large-scale electromagnetic fields combine with strong gravity. Equatorial as well as off-equatorial toroidal structures are among such…
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 geometry of reflection of a massive point-like particle at conic section boundaries. Thereby the particle is subjected to a central force associated with either a Kepler or Hooke potential. The conic section is assumed to have…
The standard closed-orbit theory is extended for the photodetachment of negative ions in a time-dependent electric field. The time-dependent photodetachment rate is specifically studied in the presence of a single-cycle terahertz pulse,…
Regular polygons are characterized as area-constrained critical points of the perimeter functional with respect to particular families of perturbations in the class of polygons with a fixed number of sides. We also review recent results in…
It is argued that, for motion in a central force field, polar reciprocals of trajectories are an elegant alternative to hodographs. The principal advantage of polar reciprocals is that the transformation from a trajectory to its polar…
Based on Newton's laws reformulated in the Hamiltonian dynamics combined with statistical mechanics, we formulate a statistical mechanical theory supporting the hypothesis of a closed oscillating universe. We find that the behaviour of the…
While it is tempting to think of closed timelike curves (CTCs) around rotating bodies such as a black hole as being "caused" by the rotation of the source, Andr\'eka et al. pointed out that the underlying physics is not as straightforward…
The effects of a paritcle's spin and electric charge on its angular momentum, energy and radius on the innermost stable circular orbit are investigated based on the particle's equations of motion in a background of the Kerr-Newmann…
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…
A conjecture of Berger states that, for any simply connected Riemannian manifold all of whose geodesics are closed, all prime geodesics have the same length. We firstly show that the energy function on the free loop space of such a manifold…
We perform numerical analysis to study the orbits described by subwavelength size particles interacting with structured light beams. Our solution to the particle dynamics considers: (i) the gradient force, (ii) the radiation pressure, and…
Orbital diamagnetism requires closed orbits according to the Liftshiftz-Kosevich theory. Therefore, one might expect that open Fermi surfaces do not have a diamagnetic response. Contrary to this expectation, we show that open orbits in…
In classical mechanics, the Kepler potential and the Harmonic potential share the following remarkable property: in either of these potentials, a bound test particle orbits with a radial period that is independent of its angular momentum.…
We examine bound orbits of particles around singly rotating black rings. We show that there exist stable bound orbits in toroidal spiral shape near the axis of the ring, and also exist stable circular orbits on the axis as special cases.…
We present a theoretical and experimental analysis of circular-like orbits made by a marble rolling on a warped spandex fabric. We show that the mass of the fabric interior to the orbital path influences the motion of the marble in a…
In this paper we consider the central force problem in the special theory of relativity. We derive the special relativistic version of the Binet equation describing the orbit of a body. Then, the motion of a planet in a solar-like system…
We show that the spectrum of orbital angular momentum in quantum mechanics consists of two parts when the underlying space has periodic boundaries. While the first part consists of the usual textbook integer quantized values, the second is…
In this paper we will refine Sacksteder's theorem for groups of orientation-preserving homeomorphisms of the circle in the case that there exists a finite orbit set. We will give a categorization of the topological possibilities for the…