Fifth and sixth integrals for optimum rocket trajectories in a central field

Six integrals of motion are obtained for the fourteenth order problem of minimum fuel rocket trajectories in an inverse square field. These integrals are for both constant exhaust velocity rockets and constant power rockets with unbounded thrust magnitude. The integrals are obtained in two different sets of variables: 1) position and velocity vectors and 2) classical orbit elements. One of the six integrals involves both the payoff and the independent variable, time. The other five integrals involve only the state and adjoint variables. Some applications of the integrals to orbit transfer problems are suggested.

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