### Abstract

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.

Original language | English |
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Number of pages | 14 |

Publication status | Published - 13 Jan 2014 |

Event | AIAA SciTech 2014 - Washington, National Harbor, Maryland, United States Duration: 13 Jan 2014 → 17 Jan 2014 |

### Conference

Conference | AIAA SciTech 2014 |
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Country | United States |

City | National Harbor, Maryland |

Period | 13/01/14 → 17/01/14 |

### Fingerprint

### Keywords

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

### Cite this

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

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

Research output: Contribution to conference › Paper

TY - CONF

T1 - Lyapunov characteristic exponent maps for multi-body space systems analysis

AU - Pagnozzi, Daniele

AU - Biggs, James

PY - 2014/1/13

Y1 - 2014/1/13

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.

KW - multibody

KW - rigid body dynamics

KW - space

KW - Lyapunov characteristic exponent

KW - Hamiltonian dynamics

UR - http://www.aiaa.org/scitech2014/

M3 - Paper

ER -