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math.DS2023
Bounded orbits for 3 bodies in
Alain Albouy, Holger R. Dullin
We consider the Newtonian 3-body problem in dimension 4, and fix a value of the angular momentum which is compatible with this dimension. We show that the energy function cannot te…
math.DS2020★ 1 cited
Relative equilibria of the 3-body problem in
Alain Albouy, Holger R. Dullin
The classical equations of the Newtonian 3-body problem do not only define the familiar 3-dimensional motions. The dimension of the motion may also be 4, and cannot be higher. We p…
math.DS2017★ 10 cited
Lambert's Theorem: Geometry or Dynamics?
Alain Albouy
Lambert's theorem (1761) on the elapsed time along a Keplerian arc drew the attention of several prestigious mathematicians. In particular, they tried to give simple and transparen…