Docking of spacecraft in an elliptical orbit

Abstract

It is an accepted fact [3] that the docking stage commences at the instant of first contact between the docking devices and is completed as soon as the vehicles are rigidly locked into a unit system. If an impact docking mechanism is used, the actual docking process is divided into two phases. The first phase includes first contact, meshing of the docking devices, and mutual stabilization of the vehicles. The second stage comprises the subsequent locking-in of the bodies. In the first phase the kinetic energy of relative motion is converted into potential energy of elastic deformations, thermal energy, vibrational energy, etc. In the second or locking phase the potential energy of the elastic deformations created in locking together two massive vehicles along a line that does not pass through the centers of mass is partially converted into kinetic energy. Our main objective here is to construct a fairly simple mathematical model of the docking of two spacecraft in an elliptical orbit. Such a model is needed primarily to ensure on-line analysis and drafting of recommendations for the suppression of vibrations of the investigated vehicle coupling in the first docking phase and to control the motions of the vehicles in the second phase with allowance for the possibility of employing vernier engines of one or both vehicles in manual control.