Celestial mechanics - nonlinear algebraic equations

 

• from J.P. Fitch, International Conference on Computer Algebra and its Applications in Theoretical Physics, p. 262-275, Dubna, (1985).

• solution of a series in a small parameter

  
  
  

• zeroth order solution , -th order solution

  
  
  
  
  
  
  
  
  
  
  
  
  

• resulting iteration scheme

  
  
  

• another example: the Kepler equation

  
  
  

• zeroth order solution -th order solution

  
  
  
  
  
  
  
  
  
  
  

  
  
  
  
  
  
  

• final solution in the form of Fourier series

  
  
  

• Fourier series are used by specialized computer algebra systems such as CAMAL and TRIGMAN