On the motion of a satellite in the vicinity of the critical inclination
Abstract
The paper treats the motion of a particle in the potential field V =  1/ (sinO) / (sinO) /r5, with J2 and J4 assumed to be small quantities of the first and the second orders, respectively, and with the value of the orbital inclination i lying in a neighborhood of ?4. The method of attack is based on the removal of the shortperiodic terms from the Hamiltonian by the von Zeipel method, followed by a Taylor series expansion of the energy integral up to quantities of the second order. As far as the Delaunay variables C', g' are concerned, the motion then becomes formally identical with that of a simple pendulum, and the solution is reduced to elliptic functions. In this form all the essential features of the motion are clearly revealed.
 Publication:

The Astronomical Journal
 Pub Date:
 December 1960
 DOI:
 10.1086/108308
 Bibcode:
 1960AJ.....65..624G