Statistics – Computation
Scientific paper
Feb 2007
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007aipc..886...90d&link_type=abstract
NEW TRENDS IN ASTRODYNAMICS AND APPLICATIONS III. AIP Conference Proceedings, Volume 886, pp. 90-99 (2007).
Statistics
Computation
1
Celestial Mechanics, Numerical Approximation And Analysis, Computational Methods In Statistical Physics And Nonlinear Dynamics
Scientific paper
During the last decade set oriented methods have been developed for the approximation and analysis of complicated dynamical behavior. These techniques do not only allow the computation of invariant sets such as attractors or invariant manifolds. Also statistical quantities of the dynamics such as invariant measures, transition probabilities, or (finite-time) Lyapunov exponents, can be efficiently approximated. All these techniques have natural applications in the numerical treatment of problems in astrodynamics. In this contribution we will give an overview of the set oriented numerical methods and how they are successfully used for the solution of astrodynamical tasks. For the demonstration of our results we consider the (planar) circular restricted three body problem. In particular, we approximate invariant manifolds of periodic orbits about the L1 and L2 equilibrium points and show an extension to the application of a continuous control force. Moreover, we demonstrate that expansion rates (finite-time Lyapunov exponents), which so far have mainly been applied in fluid dynamics, can provide useful information on the qualitative behavior of trajectories in the context of astrodynamics. The set oriented numerical methods and their application to astrodynamical problems discussed in this contribution serve as further important steps towards understanding the pathways of comets or asteroids and the design of energy-efficient trajectories for spacecraft.
Dellnitz Michael
Padberg Kathrin
Post Marcus
Thiere Bianca
No associations
LandOfFree
Set Oriented Approximation of Invariant Manifolds: Review of Concepts for Astrodynamical Problems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Set Oriented Approximation of Invariant Manifolds: Review of Concepts for Astrodynamical Problems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Set Oriented Approximation of Invariant Manifolds: Review of Concepts for Astrodynamical Problems will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-734680