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Lyapunov characteristic exponent maps for multi-body space systems analysis

Pagnozzi, Daniele and Biggs, James (2014) Lyapunov characteristic exponent maps for multi-body space systems analysis. In: AIAA SciTech 2014, 2014-01-13 - 2014-01-17, Washington.

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    Abstract

    This paper investigates the natural dynamics of a space multibody system in orbit around a celestial body using modern dynamical systems theory. In particular Lyapunov Characteristic Exponent (LCE) maps, which are used in celestial mechanics and fluid dynamics, are here applied to a multi-body system to analyse different qualitative behaviours. Complemented with phase diagrams and Poincare maps, LCE maps are shown to be an extremely useful global visualisation tool. Such a map reduces the order of the problem, condensing quantities of information into a lower-dimensional image. Here, a simple example is considered to demonstrate the usefulness of LCE maps with the aim of using it on more complex, realistic cases in the future. For this simple example a Hamiltonian formulation is derived to facilitate an analytical analysis of the systems equilibria and their nonlinear stability and to aid the validation of the numerical results.