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TECHNICAL PAPERS

# Dynamic Modeling and Simulation of Satellite Tethered Systems

[+] Author and Article Information
Kalyan K. Mankala

Department of Mechanical Engineering, University of Delaware, Newark, DE 19716mankala@me.udel.edu

Sunil K. Agrawal

Department of Mechanical Engineering, University of Delaware, Newark, DE 19716agrawal@me.udel.edu

J. Vib. Acoust 127(2), 144-156 (Jun 28, 2004) (13 pages) doi:10.1115/1.1891811 History: Received May 05, 2003; Revised June 28, 2004

## Abstract

The objective of this paper is to study the dynamic simulation of a tether as it is deployed or retrieved by a winch on a satellite orbiting around earth. In an effort to understand the problem incrementally, the following three models were developed: (a) Model 1: A tether with constant length moves on earth in the plane of constant gravity; (b) Model 2: A tether is deployed from a drum on earth in the plane of constant gravity, i.e., length of the cable changes during deployment; (c) Model 3: A tether is deployed from a drum on an orbiting satellite. These models have been chosen to bring different aspects as well as levels of difficulty in the analysis. For example, in Model 1, the length of cable is fixed and the gravity direction is constant during motion. The equations of motion for this model are derived using Newton’s laws and Hamilton’s principle to show the equivalence of the two methods. In Model 2, free length of the cable changes during deployment. The changing length of the cable introduces coupled nonlinearities into the motion. Model 3 includes the orbital effect on the motion of deployed cable. Each of these three dynamic models characterized by partial differential equations are first converted to a finite number of ordinary differential equations using Ritz’s procedure and are then numerically integrated using Matlab ODE solvers.

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## Figures

Figure 10

Model 3 (run 1): simulation of tether subsatellite system with constant length tether. (a) The tether motion in the orbital plane. (b) Tether motion with x axis of (a) zoomed. (c) The drum motion (tether deployment) ξ1(t). (d) Cable tension at the support point over time.

Figure 11

Model 3 (run 2): free deployment of subsatellite from radial configuration. (a) The tether motion in the orbital plane. (b) Tether configurations in tether attached local frame. (c) The drum motion (tether deployment coordinate) ξ1(t). (d) Cable tension at the support point over time.

Figure 12

Model 3 (run 3): free deployment of subsatellite from radial configuration with deployable tether length limited to 60m. (a) The tether motion in the orbital plane. (b) Tether configurations in tether attached local frame. (c) The drum motion (tether deployment coordinate) ξ1(t). (d) Cable tension at the support point over time.

Figure 13

Model 3 (run 4): retrieval of subsatellite from radial configuration. (a) The tether motion in the orbital plane. (b) Tether configurations in tether attached local frame. (c) The drum motion (tether deployment coordinate) ξ1(t). (d) Cable tension at the support point over time.

Figure 1

A schematic of phases of ROGER mission according to ESA (from ESA sponsered ROGER project meetings)

Figure 2

A sketch of a constant length tether moving in the vertical plane under constant gravity

Figure 3

A sketch of the system with variable length tether under constant gravity

Figure 4

A schematic of a tether deployed from a drum in circular orbit

Figure 5

Model 1 (run 1): free fall under gravity with area of cross section of tether, A=πmm2 (so μ¯=0.0045kg∕m). (a) The tether motion in the vertical plane. (b) Tether configuration at t=3s in tether attached local frame. (c) The tether change in length over time. (d) Cable tension at the support point over time.

Figure 6

Model 1 (run 2): free fall under gravity with area of cross section of tether, A=10πmm2 (so μ¯=0.045kg∕m). (a) The tether motion in the vertical plane. (b) Tether configuration at t=3s in tether attached local frame. (c) The tether change in length over time. (d) Cable tension at the support point over time.

Figure 7

Model 2 (run 1): free fall under gravity. (a) The tether motion in the vertical plane. (b) Tether configuration in tether attached local frame. (c) Tether deployment over time. (d) Cable tension at the support point over time.

Figure 8

Model 2 (run 2): free fall under gravity with deployable tether length limited to 60m. (a) The tether motion in the vertical plane. (b) Tether configuration in tether attached local frame. (c) Tether deployment over time. (d) Cable tension at the support point over time.

Figure 9

Model 2 (run 3): tether retrieval from an initial deployed length of 60m using an external drum torque of 97.5Nm. (a) The tether motion in the vertical plane. (b) Tether configuration at t=10s in tether attached local frame. (c) Tether deployment over time. (d) Cable tension at the support point over time.

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