Numerical analysis of periodic motion of tethered satellite systems.

Abstract

Momentum exchange space tethers offer an alternative solution to orbital maneuvering and attitude control. However, the issue of induced tether vibrations remains one of the major challenges. Large oscillations in the tether can cause it to break. A theoretical model of a satellite system is proposed as a way to examine the various damping systems that work to reduce satellite liberations. The challenges with existing software include costs, uncommon programming languages, and hardware availability. To combat these obstacles, a new model was constructed using MATLAB due to its low student license cost, prevalence in college curricula and mathematical robustness. The numerical model considered in this study utilizes Lagrange’s Equations as a method to obtain the equations of motion for the system in a low Earth orbit and the rotation about the system’s center of mass. It can be shown the motion of the system in orbit and in rotation can be described through a set of secord order non-linear ordinary differential equations. To approximate the positions of the two satellite masses, Runge-Kutta fourth-order method is used. Simulations were then run to examine vibrations in the tether under different mission parameter sets. Sub-satellite mass, tether length, and orbital altitude of the main satellite were varied over a range of values for three different tether materials. This was done to determine general trends and relationships between these four mission parameters in order to optimize dampening of the vibrations in the tether. It can be shown that decreasing sub-satellite mass leads to smaller oscillations in the tether. Orbital altitude and tether length both have specific nodes where tether vibrations are minimized. Overall system behavior does not change with tether material density or strength.