Gravity Assist Space Pruning Based on Differential Algebra
AbstractIn this paper a differential algebra version of the gravity assist space pruning
algorithm is presented. The use of differential algebraic techniques is proposed to overcome
the two main drawbacks of the existing algorithm, i.e., the steep increase of the number of
function evaluations with the number of planets involved in the transfer, and the use of a
bounding procedure that relies on Lipschitzian tolerances. Differential algebra allows us to
process boxes in place of grid points, and to substitute pointwise evaluations of the constraint
functions with their Taylor expansions. Thanks to the particular instance of multi-gravity
assist problems dealt with, all the planet-to-planet legs can be treated independently, and
forward and backward constraining can be applied. The proposed method is applied to preprocess
the search space of sample interplanetary transfers and it also serves as a stepping
stone towards a fully rigorous treatment of the pruning process based on Taylor models.
R. Armellin, P. Di Lizia, F. Topputo, M. Lavagna, F. Bernelli-Zazzera, M. Berz,
Celestial Mechanics and Dynamical Astronomy, 106,1 (2010) 1-24
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