Related papers: Periods of N-body Systems Determined Through Dimen…
Inspired by amazing result obtained by Semay \cite{semay-1}, this study revisits generalised Kepler's third law of an n-body system from the perspective of dimension analysis. To be compatible with Semay's quantum n-body result, this letter…
Three-body and n-body problems in celestial mechanics are age-old and challenging puzzles. In recent years, several breakthroughs are made in finding periodic orbits for three-body problem. And Bohua Sun proposed a conjecture on Kepler's…
This study considers the periodic orbital period of an n-body system from the perspective of dimension analysis. According to characteristics of the n-body system with point masses $(m_1,m_2,...,m_n)$, the gravitational field parameter,…
The Kepler's third law is a relation between the period and the energy of two classical particles interacting via a gravitational potential. Recent works showed that this law could be extended, at least approximately, to classical…
A generalization of the Kepler's third law has been proposed by BoHua Sun for $N$-body periodic orbits in a Newtonian gravitation field. In this paper, it is shown that this formula can apply for a quantum system of $N$ self-gravitating…
We provide the differential equations that generalize the Newtonian N-body problem of celestial mechanics to spaces of constant Gaussian curvature, k, for all k real. In previous studies, the equations of motion made sense only for k…
We present results of numerical calculations showing a three-body orbit's period's $T$ dependence on its topology. This dependence is a simple linear one, when expressed in terms of appropriate variables, suggesting an exact mathematical…
Despite the huge number of research into the three-body problem in physics and mathematics, the study of this problem still remains relevant both from the point of view of its broad application and taking into account its fundamental…
We generalize the curved $N$-body problem to spheres and hyperbolic spheres whose curvature $\kappa$ varies in time. Unlike in the particular case when the curvature is constant, the equations of motion are non-autonomous. We first briefly…
We present an innovative approach to dimensional analysis, based on a general representation theorem for complete quantity functions admitting a covariant scalar representation; this theorem is in turn grounded in a purely algebraic theory…
We consider a Kepler problem in dimension two or three, with a time-dependent $T$-periodic perturbation. We prove that for any prescribed positive integer $N$, there exist at least $N$ periodic solutions (with period $T$) as long as the…
In this paper we give examples of applications of general methods of quantization by symmetrization of classical integrable systems, which have been illustrated in two previous works by the same authors. We consider two classes of systems…
We investigate quantum effects in the evolution of general systems. For studying such temporal quantum phenomena, it is paramount to have a rigorous concept and profound understanding of the classical dynamics in such a system in the first…
Let a number, N, of particles interact classically through Newton's Laws of Motion and Newton's inverse square Law of Gravitation. The resulting equations of motion provide an approximate mathematical model with numerous applications in…
We consider the problem of the motion of $N$ bodies in a self-gravitating system in two spacetime dimensions. We point out that this system can be mapped onto the quantum-mechanical problem of an N-body generalization of the problem of the…
The article formulates the classical three-body problem in conformal-Euclidean space (Riemannian manifold), and its equivalence to the Newton three-body problem is mathematically rigorously proved. It is shown that a curved space with a…
A mathematical model is given for the occurrence of preferred orbits and orbital velocities in a Keplerian system. The result can be extended into energies and other properties of physical systems. The values given by the model fit closely…
The curved spacetime geometry of a system of two point masses moving on a circular orbit has a helical symmetry. We show how Kepler's third law for circular motion, and its generalization in post-Newtonian theory, can be recovered from a…
This study presents a general alternative scheme of the procedure and necessary conditions for solving the $n$-body problem. The presented solution is not a solution of the classical problem, where the initial conditions of positions and…
In this contribution, we discuss three situations in which complete integrability of a three dimensional classical system and its quantum version can be achieved under some conditions. The former is a system with axial symmetry. In the…