Bifurcations of plane with three-dimensional periodic orbits in the elliptic restricted problem

Robin, I.A.

Celestial Mechanics 23(1): 97-106


ISSN/ISBN: 1572-9478
Accession: 082107589

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We show that the procedure employed in the circular restricted problem, of tracing families of three-dimensional periodic orbits from vertical self-resonant orbits belonging to plane families, can also be applied in the elliptic problem. A method of determining series of vertical bifurcation orbits in the planar elliptic restricted problem is described, and one such series consisting of vertical-critical orbits (a v=+1) is given for the entire range (0,1/2) of the mass parameter μ. The initial segments of the families of three-dimensional orbits which bifurcate from two of the orbits belonging to this series are also given.