The invariant equations of the threebody problem for aligned bodies
Abstract
On the basis of the invariance of the equation lambda equals lv, where the square of v is equal to the sum of the squares of p, with respect to the transformation q equals rho(Q), p equals P/square root of rho, where rho is an arbitrary function of position and velocity, as pointed out by Cartan, the author derives the equations of the rectilinear threebody problem in LagrangeJacobi variables by using only the invariants of this transformation. Results are obtained generalizing the case of zero energy and suggesting a connection between the motions of triple collision and parabolic motions.
 Publication:

Academie des Sciences Paris Comptes Rendus Serie Sciences Mathematiques
 Pub Date:
 April 1976
 Bibcode:
 1976CRASM.282..927N
 Keywords:

 Celestial Mechanics;
 Invariance;
 Orbital Mechanics;
 Three Body Problem;
 Transformations (Mathematics);
 Cartesian Coordinates;
 Differential Equations;
 Equations Of Motion;
 Integral Equations;
 Lagrange Similarity Hypothesis;
 Particle Collisions;
 Astrodynamics