TY - JOUR
A2 - Abudiab, Mufid
AU - Leeghim, Henzeh
AU - Kim, Donghoon
AU - Turner, James
PY - 2013
DA - 2013/11/26
TI - Solution for Nonlinear Three-Dimensional Intercept Problem with Minimum Energy
SP - 435725
VL - 2013
AB - Classical orbit intercept applications are commonly formulated and solved as Lambert-type problems,where the time-of-flight (TOF) is prescribed. For general three-dimensional intercept problems,selecting a meaningful TOF is often a difficult and an iterative process. This work overcomesthis limitation of classical Lambert’s problem by reformulating the intercept problem in terms ofa minimum-energy application, which then generates both the desired initial interceptor velocityand the TOF for the minimum-energy transfer. The optimization problem is formulated byusing the classical Lagrangian f and g coefficients, which map initial position and velocity vectorsto future times, and a universal time variable x. A Newton-Raphson iteration algorithm is introducedfor iteratively solving the problem. A generalized problem formulation is introduced forminimizing the TOF as part of the optimization problem. Several examples are presented, and theresults are compared with the Hohmann transfer solution approaches. The resulting minimum-energy intercept solution algorithm is expected to be broadly useful as a starting iterative for applications spanning: targeting, rendezvous, interplanetary trajectory design, and so on.
SN - 1024-123X
UR - https://doi.org/10.1155/2013/435725
DO - 10.1155/2013/435725
JF - Mathematical Problems in Engineering
PB - Hindawi Publishing Corporation
KW -
ER -