Dynamics of a Tether System Connected to an Irregularly Shaped Celestial Body
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Dynamics of a Tether System Connected to an Irregularly Shaped Celestial Body Mohammad Jalali Mashayekhi1 · Arun K. Misra2 · Mehdi Keshmiri3
© American Astronautical Society 2016
Abstract The problem of pendular oscillations of a tether attached to an irregularly shaped celestial body is studied in this paper. The dynamic analysis of the system is performed by examining the phase plane trajectories. The effect of the tether length as well as the higher order terms in the gravitational potential of the celestial body on the tether dynamics is investigated. It is demonstrated that consideration of the finite size of the celestial body can have significant effects on the tether dynamics, while the effect of the asphericity of the celestial body on the tether dynamics is negligible. This study is of practical relevance for asteroid deflection using tethers, as well as for the development of space elevators on small planets/moons. Keywords Tethered satellite systems · Asteroid deflection · Spacecraft dynamics · Space elevator
Mohammad Jalali Mashayekhi
[email protected] 1
Department of Mechanical and Industrial Engineering, University of Toronto, 5 King’s College Road, M5S 3G8, Toronto, ON, Canada
2
Department of Mechanical Engineering, McGill University, 817 Sherbrooke Street West, H3A 0C3 Montreal, QC, Canada
3
Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran
J of Astronaut Sci
Introduction Dynamics of a tether system attached to an irregularly shaped celestial body, which is basically a more complex form of the problem of the simple pendulum, is investigated in this paper. The finite size of the main celestial body (e.g. an asteroid) may affect the system dynamics via the offset between the point of tether attachment and the center of mass of the body. The irregular shape of the celestial body influences the tether dynamics through the higher order harmonics in the gravitational potential. The results of this study can be useful for developing a more accurate model for asteroid deflection using a tether-ballast attachment. In the existing literature on asteroid deflection using tethers, the asteroid is usually modeled as a point mass [1, 2, 4], although consideration of the finite size of the asteroid appears to be an essential part of a reliable asteroid deflection model. Furthermore, this study is also of practical importance to the development of space elevators on small planets/moons [3, 5–8]. This paper is focused on the dynamics of the tether itself. The tether dynamics is strongly influenced by the rotational motion of the celestial body. The rotational period of celestial bodies such as asteroids, are usually of the order of a few hours and is much smaller than their orbital period, which is of the order of a few years. In this paper the tether dynamics is studied within a small time scale compared to the orbital period of the celestial body. Hence, the effect of the orbital motion of the celestial body on the tether dynamics is neglect
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