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

## Palavras-chave:

nonlinear dynamics, rigid bodies, mathematical modeling, space tether, tethered satellites## 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.