Set oriented approximation of invariant manifolds: Review of concepts for astrodynamical problems

Research output: Contributions to collected editions/worksArticle in conference proceedingsResearchpeer-review

Authors

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.

Original languageEnglish
Title of host publicationNew Trends in Astrodynamics and Applications III : Princeton, New Jersey, 16-18 August 2006
EditorsEdward Belbruno
Number of pages10
Place of PublicationPrinceton, New Jersey
PublisherAmerican Institute of Physics Inc.
Publication date07.02.2007
Pages90-99
ISBN (print)0-7354-0389-9, 978-0-7354-0389-5
DOIs
Publication statusPublished - 07.02.2007
Externally publishedYes
EventInternational Conference on New Trends in Astrodynamics and Applications - American Institute of Physics, University princeton, Princeton, United States
Duration: 16.08.200618.08.2006
Conference number: 3

    Research areas

  • Finite-time Lyapunov exponents, Hamiltonian systems, Invariant manifolds, Reachable sets, Set oriented numerics, Space mission design, Three body problem
  • Mathematics

DOI

Recently viewed

Publications

  1. Human–learning–machines: introduction to a special section on how cybernetics and constructivism inspired new forms of learning
  2. A sensor fault detection scheme as a functional safety feature for DC-DC converters
  3. Mapping the intersection of planetary boundaries and environmentally extended input-output analysis: A systematic literature review
  4. Computational modeling of amorphous polymers
  5. Dynamic Lot Size Optimization with Reinforcement Learning
  6. The delay vector variance method and the recurrence quantification analysis of energy markets
  7. Dispatching rule selection with Gaussian processes
  8. Computing regression statistics from grouped data
  9. Analysis of long-term statistical data of cobalt flows in the EU
  10. Image compression based on periodic principal components
  11. Gaussian processes for dispatching rule selection in production scheduling
  12. Digging into the roots
  13. Gain Adaptation in Sliding Mode Control Using Model Predictive Control and Disturbance Compensation with Application to Actuators
  14. Challenge-oriented policy making and innovation systems theory: reconsidering systemic instruments
  15. A PD regulator to minimize noise effect using a minimal variance method for soft landing control of an electromagnetic valve actuator
  16. Methodological support for the selection of simplified equations of state for modeling technical fluids
  17. Faulty Process Detection Using Machine Learning Techniques
  18. Development and evaluation of a training program for dialysis nurses - An intervention study
  19. Measuring Learning Styles with Questionnaires Versus Direct Observation of Preferential Choice Behavior in Authentic Learning Situations
  20. Extending talk on a prescribed discussion topic in a learner-native speaker eTandem learning task
  21. A Multimethod Latent State-Trait Model for Structurally Different and Interchangeable Methods
  22. Extraction of finite-time coherent sets in 3D Rayleigh-Benard Convection using the dynamic Laplacian
  23. Towards an open question answering architecture
  24. Knowledge transfer during the integration of knowledge-intensive acquisitions
  25. Development and application of a simplified sampling method for volatile polyfluorinated alkyl substances in indoor and environmental air
  26. Earnings Less Risk-Free Interest Charge (ERIC) and Stock Returns—A Value-Based Management Perspective on ERIC’s Relative and Incremental Information Content
  27. Introduction to Automatic Imitation
  28. SoilTemp: A global database of near-surface temperature
  29. Science-Related Outcomes
  30. The complexity of integrated flood management
  31. Negotiating boundaries through reality shows
  32. An empirically grounded ontology for analyzing IT-based interventions in business ecosystems
  33. Influence of Mg content in Al alloys on processing characteristics and dynamically recrystallized microstructure of friction surfacing deposits
  34. The development of an eco-label for software products

Press / Media

  1. Rio+20