Lyapunov characteristic exponent maps for multi-body space systems analysis

Daniele Pagnozzi, James Biggs

Research output: Contribution to conferencePaper

1 Citation (Scopus)

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.
LanguageEnglish
Number of pages14
Publication statusPublished - 13 Jan 2014
EventAIAA SciTech 2014 - Washington, National Harbor, Maryland, United States
Duration: 13 Jan 201417 Jan 2014

Conference

ConferenceAIAA SciTech 2014
CountryUnited States
CityNational Harbor, Maryland
Period13/01/1417/01/14

Fingerprint

Systems analysis
Hamiltonians
System theory
Fluid dynamics
Phase diagrams
Mechanics
Dynamical systems
Orbits
Visualization

Keywords

  • multibody
  • rigid body dynamics
  • space
  • Lyapunov characteristic exponent
  • Hamiltonian dynamics

Cite this

Pagnozzi, D., & Biggs, J. (2014). Lyapunov characteristic exponent maps for multi-body space systems analysis. Paper presented at AIAA SciTech 2014, National Harbor, Maryland, United States.
Pagnozzi, Daniele ; Biggs, James. / Lyapunov characteristic exponent maps for multi-body space systems analysis. Paper presented at AIAA SciTech 2014, National Harbor, Maryland, United States.14 p.
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Pagnozzi, D & Biggs, J 2014, 'Lyapunov characteristic exponent maps for multi-body space systems analysis' Paper presented at AIAA SciTech 2014, National Harbor, Maryland, United States, 13/01/14 - 17/01/14, .

Lyapunov characteristic exponent maps for multi-body space systems analysis. / Pagnozzi, Daniele; Biggs, James.

2014. Paper presented at AIAA SciTech 2014, National Harbor, Maryland, United States.

Research output: Contribution to conferencePaper

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AU - Biggs, James

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N2 - 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.

AB - 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.

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Pagnozzi D, Biggs J. Lyapunov characteristic exponent maps for multi-body space systems analysis. 2014. Paper presented at AIAA SciTech 2014, National Harbor, Maryland, United States.