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Victor Hertel edited this page Jun 3, 2018 · 8 revisions

HaloPropagation Wiki

Introduction

The HaloPropagation Wiki contains general information on the numerical determination and propagation of periodic halo orbits. In addition, further possibilities such as various continuation schemes and their application as well as the structure of this tool including syntax rules are presented. Detailed background information on Lagrangian Point Orbits, including an overview of Orbit Types in cis-lunar Space, Classification of Halo Orbits, the Dynamical Models and Dynamical Systems Theory can be downloaded as a PDF document here.

It is recommended to start with the chapters of the Introduction chapter to obtain an overview and to get familiar with general algorithms and principles:

  1. Numerical Investigation of Periodic Halo Orbits
  2. Orbit Continuation Methods
  3. Program Structure
  4. Syntax

Afterwards the Halo Trajectory Design and Continuation Tool can be used properly. For further understanding, as already mentioned, see the Background Information.

The Wiki and further background information can be downloaded in PDF version here.

Introduction

Background Information

  1. Orbit Types in cis-lunar Space
    • Keplerian Orbits
      • Low Lunar Orbit
      • Elliptical Lunar Orbit
      • Frozen Lunar Orbit
    • Lagrangian Point Orbits
      • Periodic Orbits
      • Quasi-Periodic Orbits
  1. Classification of Halo Orbits
    • Halo Orbit Families
      • L1 Halo Family
      • L2 Halo Family
      • L3 Halo Family
    • Near Rectilinear Halo Orbit
  1. Dynamical Models
    • n-Body Problem
    • Three Body Problem
    • Circular Restricted Three Body Problem
      • Assumptions
      • Coordinate Systems
      • Non-dimensionalization
      • Equations of Motion
      • Jacobi Constant
      • First Order Analytical Approximations for Motion in the Vicinity of Libration Points
      • Approximate Periodic Solutions
  1. Dynamical Systems Theory
    • State Transition Matrix
    • Differential Corrections
    • Periodic Halo Orbit Computation
    • Continuation of an Halo Orbit Family
      • Natural Parameter Continuation
      • Pseudo-Arclength Continuation
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