## Abstract

The minimum-propellant deterministic guidance law for bounded-thrust, constant jetexhaust velocity, spacecrafts is developed using the neighboring extremal theory. Minimization of the first-order variation in cost between a multi-burn nominal extremal and the perturbed trajectory eliminates all correction strategies except small changes in the nominal thrust-on, thrust-off times and small rotations of the thrust vector. Optimal values of these corrective controls for fixed values of initial state deviations, δx_{0}, are found by minimizing the second variation in cost subject to the variational state and adjoint equations - an accessory minimum problem. The solution takes the linear feedback form δu=A^{-1}_{22}A_{21}δx_{0}, where the matrices A_{22} and A_{21} are functions only of transition matrices calculated along the nominal trajectory. The solution is applied to a three-burn Earth-Mars transfer.

Original language | English (US) |
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Pages (from-to) | 261-281 |

Number of pages | 21 |

Journal | Celestial Mechanics |

Volume | 5 |

Issue number | 3 |

DOIs | |

State | Published - May 1 1972 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Astronomy and Astrophysics
- Space and Planetary Science