Lecture Notes

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.

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)