An outline of the derivation of a set of variation of parameter equations by the use of Lagrange's brackets, which describe the perturbed motion of a space vehicle. These equations are integrated to obtain a set of state transformation equations which are used in conjunction with the method of dynamic programming to optimize a multi-stage orbit transfer process. Three special cases of the multi-stage process are discussed: a single-stage process, a two-stage process, and a special form of performance criterion.
This report is part of the RAND Corporation paper series. The paper was a product of the RAND Corporation from 1948 to 2003 that captured speeches, memorials, and derivative research, usually prepared on authors' own time and meant to be the scholarly or scientific contribution of individual authors to their professional fields. Papers were less formal than reports and did not require rigorous peer review.
The RAND Corporation is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.