MATHEMATICAL MODELING AND DYNAMICS OF TWO TETHERED SATELLITES: RIGID BODY APPROACH

Resumo

A two-dimensional nonlinear mathematical model for two tethered satellites is developed.
This complex system comprises of a long cable (also known as tether or, in this case, space tether)
connecting two masses (satellites). Tethered satellites can be used in a variety of space applications
such as electrodynamic propulsion, energy harvesting, momentum exchange, artificial gravity, etc. As
a first rough mathematical model, the cable connecting the satellites is approximated by two
connecting rod-like rigid bodies. If these rods are not aligned, it is assumed that the cable is not
stretched (i.e. the cable is not under tension). This is an undesirable situation for this type of system.
The whole system is allowed to rotate and translate only on a two-dimensional space. The set of
ordinary differential governing equations of motion are obtained using the Lagrange ́s equations
approach. These nonlinear equations are numerically integrated and the dynamics of the system is
investigated under several practical circumstances.