### Abstract

Higher order differential inclusion (HODI) is a new modeling technique that is applied to the modeling and optimization of spacecraft trajectories. The spacecraft equations-of-motion are mathematically manipulated into differential constraints that remove explicit appearance of the control variables (e.g., thrust direction and magnitude) from the problem statement. These constraints are transformed into a nonlinear programming problem by using higher order approximations of the derivatives of the states. In this work, the new method is first applied to a simple example to illustrate the technique and then to a three-dimensional, propellant-minimizing, Low-Earth-Orbit to Geosynchronous-Earth-Orbit spacecraft transfer problem. Comparisons are made with results obtained using an established modeling technique.

Original language | English (US) |
---|---|

Pages (from-to) | 377-395 |

Number of pages | 19 |

Journal | Advances in the Astronautical Sciences |

Volume | 102 I |

State | Published - Dec 1 1999 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Aerospace Engineering
- Space and Planetary Science

### Cite this

*Advances in the Astronautical Sciences*,

*102 I*, 377-395.

**Optimal spacecraft trajectories via higher order differential inclusions.** / Coverstone, Victoria; Hartman, C. A.; Herman, A. L.; Spencer, D. B.

Research output: Contribution to journal › Article

*Advances in the Astronautical Sciences*, vol. 102 I, pp. 377-395.

}

TY - JOUR

T1 - Optimal spacecraft trajectories via higher order differential inclusions

AU - Coverstone, Victoria

AU - Hartman, C. A.

AU - Herman, A. L.

AU - Spencer, D. B.

PY - 1999/12/1

Y1 - 1999/12/1

N2 - Higher order differential inclusion (HODI) is a new modeling technique that is applied to the modeling and optimization of spacecraft trajectories. The spacecraft equations-of-motion are mathematically manipulated into differential constraints that remove explicit appearance of the control variables (e.g., thrust direction and magnitude) from the problem statement. These constraints are transformed into a nonlinear programming problem by using higher order approximations of the derivatives of the states. In this work, the new method is first applied to a simple example to illustrate the technique and then to a three-dimensional, propellant-minimizing, Low-Earth-Orbit to Geosynchronous-Earth-Orbit spacecraft transfer problem. Comparisons are made with results obtained using an established modeling technique.

AB - Higher order differential inclusion (HODI) is a new modeling technique that is applied to the modeling and optimization of spacecraft trajectories. The spacecraft equations-of-motion are mathematically manipulated into differential constraints that remove explicit appearance of the control variables (e.g., thrust direction and magnitude) from the problem statement. These constraints are transformed into a nonlinear programming problem by using higher order approximations of the derivatives of the states. In this work, the new method is first applied to a simple example to illustrate the technique and then to a three-dimensional, propellant-minimizing, Low-Earth-Orbit to Geosynchronous-Earth-Orbit spacecraft transfer problem. Comparisons are made with results obtained using an established modeling technique.

UR - http://www.scopus.com/inward/record.url?scp=0039129186&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0039129186&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0039129186

VL - 102 I

SP - 377

EP - 395

JO - Advances in the Astronautical Sciences

JF - Advances in the Astronautical Sciences

SN - 1081-6003

ER -