6533b7d8fe1ef96bd1269765

RESEARCH PRODUCT

Collision Orbits in the Isosceles Rectilinear Restricted Problem

R. B. OrellanaJ. Martínez Alfaro

subject

SingularityClassical mechanicsBounded functionMathematical analysisIsosceles triangleGravitational singularityNegative energyFunction (mathematics)Stable manifoldMathematicsBlowing up

description

In the study of the Collinear Three-Body Problem, McGehee (1974) introduced a new set of coordinates which had the effect of blowing up the triple collision singularity. Subsequently, his method has been used to analyze some other collision or singularities. Recently, Wang (1986) introduced another transformation which differs from the McGehee’s coordinates in the fact that the blowing-up factor is now the potential function, U, instead of the moment of inertia, I. Meyer and Wang (1993) have applied this method to the Restricted Isosceles Three-body Problem with positive energy and Cors and Llibre (1994) to the hyperbolic restricted three-body problem. In this paper we study the singularities of this problem (IRRP), due to collisions, in the case of negative energy by means of a modified version of McGehee’s coordinates. Moreover, we remove the singularities due to a velocity not bounded.

yearjournalcountryeditionlanguage
1995-01-01
https://doi.org/10.1007/978-1-4899-1085-1_37