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.

Lyapunov characteristic exponent maps for multi-body space systems analysis

BIGGS, JAMES DOUGLAS
2014-01-01

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.
2014
AIAA Guidance, Navigation, and Control Conference - SciTech 2014
9781600869624
Hamiltonian; Lyapunov characteristic exponent; Multibody; Rigid body dynamics; Space; Aerospace Engineering; Control and Systems Engineering
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/974506
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