A Comparative Study of Newtonian, Kustaanheimo/Stiefel, and Sperling/Burdet Optimal Trajectories
Abstract
An optimal trajectory problem is formulated in each of three sets of equations, and the resulting solutions are numerically compared. The three formulations are the classical Newtonian (N), the Kustaanheimo/Stiefel (K/S), and the Sperling/Burdet (S/B). The last two solutions are first regularized by the classical Sundman technique and the K/S solution is transformed before the optimization problem is posed. A novel technique is developed for generating initial control vectors for each solution. Numerically generated derivatives (central differences) are used by a type of gradient, NewtonRaphson iterator to converge the twopoint boundary value problems. The results indicate that, although the K/S and S/B formulations are more difficult to express mathematically than the Newtonian formulation, the transformed solutions are significantly more numerically stable than the Newtonian solution when the perturbing acceleration is less than a minimum value (T/W _{o}=0.05 for the particular example problem treated).
 Publication:

Celestial Mechanics
 Pub Date:
 November 1975
 DOI:
 10.1007/BF01228565
 Bibcode:
 1975CeMec..12..297J