The effect of climber initial velocity on orbital space elevator dynamics

Abstract

This research is devoted to the problem of delivering a small payload to the Earth from the orbit using an orbital space elevator, which consists of two space stations connected by a massless tether and a passive climber moving along the tether. The aim of the work is to study the possibility of transferring the climber from one end of the orbital elevator to the other end due to its initial velocity. The mathematical model of the mechanical system is constructed using the Lagrange equation of the second kind. An analytical expression, which depends on the parameters of the mechanical system and determines the required initial velocity, was found using a simplified mathematical model that does not take into account the bending of the tether. The validity of the expression was verified using the original mathematical model. The analysis of the system motion was carried out, and recommendations on its mass-geometric parameters choice were given.