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Dynamics of a particle moving along an orbital tower

McInnes, C.R. (2005) Dynamics of a particle moving along an orbital tower. Journal of Guidance, Control and Dynamics, 28 (2). pp. 380-382. ISSN 0731-5090

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The concept of an orbital tower has been discussed in the literature by many authors over a number of years. Although the concept is clearly futuristic, interest has recently been revived as a result of advances in materials science (for example, see Refs. 1-4). In this Note, a simple model of the dynamics of a particle moving along an orbital tower is considered. First, it is demonstrated that at synchronous radius there exists a hyperbolic fixed point, resulting in an unstable equilibrium and a potential barrier that a particle must cross. The fixed point is an equilibrium point in the phase space, which represents the dynamics of the particle. It is shown that the addition of friction does not remove the hyperbolic fixed point, but merely modifies its instability timescale. Finally, it is shown that friction leads to phase paths converging asymptotically to a single manifold in the phase space of the problem. An approximation to this manifold is constructed. The analysis provides some insight into the practical application of orbital towers for the launch and retrieval of payloads.