On dynamical formulation of a tethered satellite system with mass transport

Two satellites connected by a long flexible tether along the earth radial direction comprise a stable equilibrium state. This research investigates the manner in which a third mass transporting from one satellite to the other disturbs the equilibrium state. A system of four equations of in-plane motion has been derived based on the assumptions that the tether remains straight between the masses and of constant length. A combination of computer subroutines DGEAR and ZANAYT is suggested for the approximate solution of the system of nonlinear differential equations with one constraint condition on the variables. Alternatively, a system of four independent differential equations are derived by eliminating the Lagrange multiplier.