Figure, problem, and page numbers in the lecture notes all refer to sections of the course textbook with relevant content.

Battin, Richard. *An Introduction to the Mathematics and Methods of Astrodynamics*. Revised ed. Reston, VA: AIAA, 1999. ISBN: 9781563473425.

LEC # | TOPICS |
---|---|

1 | The two-body problem (PDF) |

2 | The two-body problem (cont.) (PDF) |

3 | Barker’s equation and Kepler’s equation (PDF) |

4 | The initial-value problem (PDF) |

5 | Euler angles (PDF) |

6 | The orbital boundary-value problem (BVP) (PDF) |

7 | Optimum orbital transfer (PDF) |

8 | Analytical and geometric properties of the BVP (PDF) |

9 | Lambert’s theorem and the Lagrange time equation (PDF) |

10 | Transformation of the BVP (PDF) |

11 | Hyperbolic orbits (PDF) |

12 | Patched conics and planetary flybys (PDF) |

13 | Gauss’s method for the time-constrained BVP (PDF) |

14 | Hypergeometric functions and continued fractions (PDF) |

15 | The fundamental ellipse of the BVP (PDF) |

16 | Non-singular “Gauss-like” method for the BVP (PDF) |

17 | The Battin-Vaughan algorithm for the BVP (PDF) |

18 | Preliminary orbit determination using Taylor series (PDF) |

19 | The state transition matrix (PDF) |

20 | Powered flight guidance (PDF) |

21 | Space navigation: the position fix (PDF) |

22 | The covariance, information, and estimator matrices (PDF) |

23 | Estimation of position and velocity in space navigation (PDF) |

24 | Basic elements of the three-body problem (PDF) |

25 | The restricted problem of three bodies (PDF) |

26 | The Clohessy-Wiltshire equations of relative motion (PDF) |

27 | Variation of parameters (PDF) |

28 | Effect of atmospheric drag on satellite orbits (PDF) |

29 | The disturbing function and Legendre polynomials (PDF) |

30 | Effect of J2 on a satellite orbit of the Earth (PDF) |

31 | The calculus of variations and lunar landing guidance (PDF) |

32 | Powered flight guidance to maximize final energy (PDF) |

33 | Runge-Kutta method of numerical integration (PDF) |