Related papers: On Langmuir's periodic orbit

Since the discovery of the figure-8 orbit for the three-body problem [Moore 1993] a large number of periodic orbits of the n-body problem with equal masses and beautiful symmetries have been discovered. However, most of those that have…

In the helium case of the classical Coulomb three-body problem in two dimensions with zero angular momentum, we develop a procedure to find periodic orbits applying two symbolic dynamics for one-dimensional and planar problems. A sequence…

The atomic model that Niels Bohr suggested in 1913 celebrated its greatest victories in connection with one-electron atoms. Among them were the isotopic spectral effect and what became known as Rydberg atoms, insights that were fully…

We present a proof of the existence of a periodic orbit for the Newtonian six-body problem with equal masses. This orbit has three double collisions each period and no multiple collisions. Our proof is based on the minimization of the…

We deduce the quantization of the atomic orbit for the hydrogen's atom model proposed by Bohr without using his hypothesis of angular momentum quantization. We show that his hypothesis can be deduced from and is a consequence of the…

Superconductors have often been described as `giant atoms'. The simplest description of atoms that heralded their quantum understanding was proposed by Bohr in 1913. The Bohr atom starts from some simple assumptions and deduces that the…

The famous three-body problem can be traced back to Newton in 1687, but quite few families of periodic orbits were found in 300 years thereafter. In this paper, we propose an effective approach and roadmap to numerically gain planar…

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…

The present paper deals with the periodic orbits generated by Lagrangian solutions of the restricted three-body problem when both the primaries are oblate bodies. We have illustrated the periodic orbits for different values of $\mu,…

A complete history of early atomic models would fill volumes, but a reasonably coherent tale of the path from mechanical atoms to the quantum can be told by focusing on the relevant work of three great contributors to atomic physics, in the…

Using a variational method, we exhibit a surprisingly simple periodic orbit for the newtonian problem of three equal masses in the plane. The orbit has zero angular momentum and a very rich symmetry pattern. Its most surprising feature is…

We numerically discovered around 100 distinct nonrelativistic collisionless periodic three-body orbits in the Coulomb potential in vacuo, with vanishing angular momentum, for equal-mass ions with equal absolute values of charges. These…

The hydrogen molecule contains the basic ingredients to understand the chemical bond, i.e, a pair of electrons. We show a step to understand The Correspondence Principle for chaotic system in the Chemical World. The hydrogen molecule is…

The Norwegian physicist Lars Vegard may have been the first to propose electron configurations for all the chemical elements, from hydrogen to uranium, on the basis of quantum atomic theory. This he did in papers of 1918-1919 in which he…

The idea of atoms is old but X-rays provided the first probe into the physical atom. Photographs of X-ray scattering from crystals -Laue spots- were the first visual proof for the physical existence of atoms arranged in a perfect geometric…

In 1956, Bott in his celebrated paper on closed geodesics and Sturm intersection theory, proved an Index Iteration Formula for closed geodesics on Riemannian manifolds. Some years later, Ekeland improved this formula in the case of convex…

We prove the existence of some types of periodic orbits for a particle moving in Euclidean three-space under the influence of the gravitational force induced by a fixed homogeneous circle. These types include periodic orbits very far and…

We present the results of a numerical search for periodic orbits of three equal masses moving in a plane under the influence of Newtonian gravity, with zero angular momentum. A topological method is used to classify periodic three-body…

We present in this work a pedagogical way of quantizing the atomic orbit for the hydrogen's atom model proposed by Bohr without using his hypothesis of angular momentum quantization. In contrast to the usual treatment for the orbital…

By introducing a new coordinate system, we prove that there are abundant new periodic orbits near relative equilibrium solutions of the N-body problem. We consider only Lagrange relative equilibrium of the three-body problem and…