Mathematics
Scientific paper
Nov 1975
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1975cemec..12..297j&link_type=abstract
Celestial Mechanics, Volume 12, Issue 3, pp.297-315
Mathematics
1
Scientific paper
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, Newton-Raphson iterator to converge the two-point 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).
No associations
LandOfFree
A Comparative Study of Newtonian, Kustaanheimo/Stiefel, and Sperling/Burdet Optimal Trajectories does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A Comparative Study of Newtonian, Kustaanheimo/Stiefel, and Sperling/Burdet Optimal Trajectories, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Comparative Study of Newtonian, Kustaanheimo/Stiefel, and Sperling/Burdet Optimal Trajectories will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-1376476