arXiv subjects

P. Lonngi

Publications and source records attributed to P. Lonngi.

2 recordsLinked to original sources

arXiv2018

Newtonian Few-Body Problem Central Configurations with Gravitational Charges of both Signs

The Newtonian n-Body Problem is modified assuming positive inertial masses but different sign for the interacting force which is assumed with the possibility of two different signs for the gravitational masses, according to the prescription two masses with same sign attract one to the other, two masses of different sign repel one to the other. As in electrostatics the signed mass is called charge. The inertial mass is always positive. The two body problem behaves as the similar Coulomb problem of charged particles with two equal charges. The solution is a central configuration with almost same behavior that the Newton two-body problem for hyperbolic orbits. The 3-Body problem was found with collinear solutions. The four body case of charged central configurations has only the planar [1] and collinear solutions.

physics.gen-ph↗

arXiv2009

Central configurations for the planar Newtonian Four-Body problem

The plane case of central configurations with four different masses is analyzed theoretically and is computed numerically. We follow Dziobek's approach to four body central configurations with a direct implicit method of our own in which the fundamental quantities are the quotient of the directed area divided by the corresponding mass and a new simple numerical algorithm is developed to construct general four body central configurations. This tool is applied to obtain new properties of the symmetric and non-symmetric central configurations. The explicit continuous connection between three body and four body central configurations where one of the four masses approaches zero is clarified. Some cases of coorbital 1+3 problems are also considered.

math-ph↗