TY - GEN
T1 - Necessary conditions for singular arcs involving multiple gravitational bodies
AU - Park, Chandeok
AU - Ross, I. Michael
AU - Yan, Hui
AU - Gong, Qi
PY - 2010
Y1 - 2010
N2 - We analyze the optimality of intermediate thrust arcs (singular arcs) of a rocket trajectory subject to gravitational forces from multiple bodies. We derive a series of necessary conditions for optimality including the generalized Legendre-Clebsche condition. We validate our derivations by showing that they are identical to Lawden's classical result if the equations of motion are reduced for a central gravitational field. As a means to illustrate the practical nature of our results, we apply them to a Moon-Earth transfer trajectory problem and show that the extremal solution is bang-singular-bang.
AB - We analyze the optimality of intermediate thrust arcs (singular arcs) of a rocket trajectory subject to gravitational forces from multiple bodies. We derive a series of necessary conditions for optimality including the generalized Legendre-Clebsche condition. We validate our derivations by showing that they are identical to Lawden's classical result if the equations of motion are reduced for a central gravitational field. As a means to illustrate the practical nature of our results, we apply them to a Moon-Earth transfer trajectory problem and show that the extremal solution is bang-singular-bang.
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M3 - Conference contribution
AN - SCOPUS:79959942413
SN - 9780877035602
T3 - Advances in the Astronautical Sciences
SP - 107
EP - 121
BT - Spaceflight Mechanics 2010 - Advances in the Astronautical Sciences
T2 - AAS/AIAA Space Flight Mechanics Meeting
Y2 - 14 February 2010 through 17 February 2010
ER -