Regularization and the Computation of Optimal Trajectories

Details Regularization and the Computation of Optimal Trajectories Regularization and the Computation of Optimal Trajectories

Sep 1970

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1970cemec...2..319t&link_type=abstract

Celestial Mechanics, Volume 2, Issue 3, pp.319-333

Computer Science

2

Scientific paper

A completely regular form for the differential equations governing the three-dimensional motion of a continuously thrusting space vehicle is obtained by using the Kustaanheimo-Stiefel regularization. The differential equations for the thrusting rocket are transformed using the K-S transformation and an optimal trajectory problem is posed in the transformed space. The canonical equations for the optimal motion in the transformed space are regularized by a suitable change of the independent variable. The transformed equations are regular in the sense that the differential equations do not possess terms with zero divisors when the motion encounters a gravitational force center. The resulting equations possess symmetry in form and the coefficients of the dependent variables are slowly varying quantities for a low-thrust space vehicle.

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