3 papers
math-ph2025
On the eigenvalues of a central configuration
Alain Albouy, Jiexin Sun
The equations of the Newtonian -body problem have a matrix form, where an matrix depending on the masses and on the mutual distances appears as a factor. The eig…
physics.class-ph2025
Does Newtonian dynamics need Euclidean space?
Alain Albouy
We present an elementary deduction of the Newtonian force from Kepler's laws. We relate it to a generalization by Jacobi of the Keplerian motion, where the Euclidean form in the pl…
math-ph2024
Note on the attraction of an ellipsoid in a spherical universe
Alain Albouy
A classical theorem states that two confocal ellipsoids, each of them endowed with a surface distribution of mass which is called homeoidal, exert the same Newtonian force on an ex…