While at George Washington University, University of Maryland and North Carolina State University, Prof. Tolson primarily taught three courses. Although the course names varied from school to school the topics were "Space Flight Orbital Mechanics", "Space Flight Guidance and Navigation" and "Analytical Mechanics." Initially, Space Flight Orbital Mechanics and Guidance and Navigation used contemporary orbital mechanics or astrodynamics books. In 1995 Prof. Tolson began writing his own book which included traditionally omitted but essential topics for practicing space flight engineers like coordinate and time systems. Further, the book was hyperlinked for easy cross referencing. Course outlines are given below.

Space Flight Orbital Mechanics

Text Book:

Space Flight Orbital Mechanics, Guidance and Navigation, R. H. Tolson, e-book

Topics covered Chapters 1-7:

• Geocentric equatorial and ecliptic coordinate systems, topocentric systems, geodetic altitude and latitude, spherical trigonometry.
• Relations among time systems including ephemeris, universal, sidereal, and atomic time.
• Integrals of the N-body, three body and two body problems.
• Details of the two body problem including solutions of Kepler's equation for elliptic, parabolic and hyperbolic orbits, universal variables.
• Three body problem, Lagrange points and stability, periodic orbits, Lagrange finite mass particular solutions.
• Orbital perturbations, Lagrange's planetary equations, Gauss's form, oblateness, drag, solar pressure and N-body effects.
• Special orbits: sun-synchronous, polar, critical inclination, geo-synchronous, frozen, constellations, GPS, Molniya.

1. Utilities to transform between various time systems: universal, sidereal, ephemeris times, and Julian date.
2. Utilities to (1) transform from various coordinate systems c anomaly ('f2E') and (2) vis-versa ('E2f') and (3) solve Kepler's equation ('kepler') for all types of orbits.
3. Procedures to calculate Keplerian orbital elements from Cartesian position and velocity considering all degenerate orbit cases.
4. Procedures to transform from orbital elements to Cartesian position and velocity including solving Kepler's and Barker's equations.
5. Procedures to study restricted three body problem libration points, periodic orbits, and Earth-Moon transfers.

Space Flight Guidance and Navigation

Text Book:

Space Flight Orbital Mechanics, Guidance and Navigation, R. H. Tolson, e-book

Topics covered: Chapters 8 & 9

• Space flight trajectories, optimal transfers, Hohmann transfers including bi-elliptic and bi-parabolic transfers, Lambert's theorem, patched conics, sphere of influence, gravity assist via planetary flyby, B-plane, propulsive requirements, pork-chop plots, Runge-Kutta single step methods, Adams-Moulton and Adams-Bashford multi-step methods, precision trajectory equations of motion.
• Navigation and orbit determination, initial orbit determination, spectroscopic binaries, information content of deep space Doppler and range measurements, optical approach data, delta differential Doppler, least squares, minimum variance, batch and sequential filter methods.
• Guidance algorithms, rendezvous, constant time of arrival and minimum delta V midcourse corrections, B-plane targeting, planetary protection bias.

1. Lambert's problem solver for all types of orbits.
2. Procedure for making pork-chop plots.
3. Procedure to determine midcourse corrections.
4. Procedure to perform initial orbit determination using classical methods.
5. Procedure for batch minimum variance differential correction.
6. Procedure for sequential filter.

Analytical Mechanics

Text Book:

Methods of Analytical Dynamics, Leonard Meirovitch, Dover 0-486-43239-4

Topics covered: Chapters 1-6

• Review of Newtonian mechanics, generalized coordinates, virtual work, Hamilton's principle, Lagrange's equations, rotating reference frames, rigid body kinematics and dynamics, geometric theory of dynamical systems, stability of linear and non-linear systems.





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Updated 10/1/2011 by RHT
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