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Technical Briefs

Dynamic Modeling of Satellite Tether Systems Using Newton’s Laws and Hamilton’s Principle

[+] 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

Atlantis Orbiter mass during mission STS-46 which performed TSS-1 experiment—lift-off mass: 116,133kg. Orbiter mass at landing: 94,711kg (data obtained from website http://www.astronautix.com/flights/sts46.htm).

Subsatellite mass during TSS-1R mission is 518kg (data obtained from website http://liftoff.msfc.nasa.gov/shuttle/sts-75/tss-1r/hw/satellite.html).

Orbiter dimensions: length 37.24m, height 17.27m, wingspan 23.79m (from http://www.boeing.com/defense-space/space/hsfe̱shuttle/facts.html).

J. Vib. Acoust 130(1), 014501 (Nov 12, 2007) (6 pages) doi:10.1115/1.2776342 History: Received June 06, 2006; Revised May 10, 2007; Published November 12, 2007

The objective of this paper is to derive the dynamic equations of a tether as it is deployed or retrieved by a winch on a satellite orbiting around Earth using Newton’s laws and Hamilton’s principle and show the equivalence of the two methods. The main feature of this continuous system is the presence of a variable length domain with discontinuities. Discontinuity is present at the boundary of deployment because of the assumption that the stowed part of the cable is unstretched and the deployed part is not. Developing equations for this variable domain system with discontinuities, specially using Hamilton’s principle, is a nontrivial task and we believe that it has not been adequately addressed in the literature.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 2

A schematic of a tether deployed from a drum in circular orbit. Tether leaves drum at an arbitrary angle β.

Grahic Jump Location
Figure 1

A Schematic of a tether deployed from a drum in circular orbit. Tether leaves drum at a constant angle.

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