Perturbation Theory

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Perturbation Theory

• The transformation from cartesian variables to
  Delaunay variables is canonical
• M, ?, and ? are coordinates and ?, h, and hz
  their momentums
• See section 4, R. Ramis, Mecánica Orbital y
  Dinámica de Actitud, ETSIA
• See chapter 8, F. T. Geyling and H. R. Westerman,
  Introduction to Orbital Mechanics, Chapter 8,
  Addison-Wesley

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Example constant radial force
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System of ODE to be solved numerically
Numerical (truncation) error g DtN, instead
DtN
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First order equations can be reduced to
integrals
Equation for M1 must be integrated after equation
for a1
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Sometimes integrals can be evaluated analytically
The parameter variations include secular and
oscilatory terms
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rmax
e
rmin
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