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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.