Initial conditions for a halo orbit

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SUMMARY

The discussion centers on calculating initial conditions for halo orbits using the third order approximation solution. Key insights are derived from the paper by Thurman and Worfolk, specifically starting from page 15, which details the Lindstedt-Poincare method. The terms \tau_1, A_x, and A_z, which include the small parameter \epsilon, are critical for these calculations. The user has successfully resolved the computation of these terms.

PREREQUISITES
  • Understanding of halo orbits in astrodynamics
  • Familiarity with the Lindstedt-Poincare method
  • Knowledge of third order approximation techniques
  • Basic grasp of perturbation theory
NEXT STEPS
  • Read the paper "Geometry of Halo Orbits" by Thurman and Worfolk
  • Study the Lindstedt-Poincare method in detail
  • Explore perturbation theory applications in astrodynamics
  • Investigate numerical methods for computing small parameters in orbital mechanics
USEFUL FOR

Aerospace engineers, astrophysicists, and students studying orbital mechanics will benefit from this discussion, particularly those focused on halo orbits and perturbation methods.

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Hey folks I'm looking into halo orbits and I have a question about how to find the initial conditions from the third order approximation solution...

A good run through of the third order solution calculation is found in this paper.
http://www.scribd.com/doc/36160757/ThurmanWorfolkGeometryHaloOrbits
The Lindstedt-Poincare part begins on page 15.

My questions are...

The final approximation includes the \tau_1, A_x and A_z terms. These all contain the small parameter \epsilon which hasn't been given a numerical value so how do I compute \tau_1, A_x and A_z?
 
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This is now solved.
 

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