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4 papers · 1 filter
A limit of nonplanar 5-body central configurations is nonplanar
Alain Albouy, Antonio Carlos Fernandes
Moeckel (1990), Moeckel and Simó (1995) proved that, while continuously changing the masses, a 946-body planar central configuration bifurcates into a spatial central configuration…
How many Keplerian arcs are there between two points of spacetime?
Alain Albouy, Antonio J. Ureña
We consider the Keplerian arcs around a fixed Newtonian center joining two prescribed distinct positions in a prescribed flight time. We prove that, putting aside the "opposition c…
Darboux inversions of the Kepler problem
Alain Albouy, Lei Zhao
While extending a famous problem asked and solved by Bertrand in 1873, Darboux found in 1877 a family of abstract surfaces of revolution, each endowed with a force function, with t…
Lambert's theorem and projective dynamics
Alain Albouy, Lei Zhao
We prove that the classical Lambert theorem about the elapsed time on an arc of Keplerian orbit extends without change to the Kepler problem on a space of constant curvature. We pr…