Science/Memorandum Series

The Memorandum Series is a compilation of handouts that I have prepared mainly as reminder (hence the name “Memorandum”) for various topics I deal with. They are also intended as teaching materials; as such, many of them contain supplemental files, e.g. software implementations of the algorithms and theory presented therein.

If you have any feedback, comments, error reports, ideas and enhancement requests regarding the Memorandum Series, do not hesitate to use my bug tracker.

M001: Keplerian Orbit Elements to Cartesian State Vectors

This Memorandum contains an algorithm for converting a traditional set of Keplerian Orbit Elements (semi-major axis, eccentricity, argument of periapsis, longitude of ascending node, inclination, and mean anomaly) to cartesian state vectors (position and velocity vector).

Keywords:
Kepler, Orbit, Elements, Cartesian, State, Vector, Rotation, Matrix

Downloads:

M002: Cartesian State Vectors to Keplerian Orbit Elements

This Memorandum contains an algorithm for converting cartesian state vectors (position and velocity vector) to a traditional set of Keplerian Orbit Elements (semi-major axis, eccentricity, argument of periapsis, longitude of ascending node, inclination, and mean anomaly).

Keywords:
Kepler, Orbit, Elements, Cartesian, State, Vector

Downloads:

M003: Trigonometric Functions

A formulary of trigonometric functions, providing the following sections:

Trigonometric functions and their definitions
Shorthands
Important values of the basic trigonometric functions
Pythagorean and related trigonometric identities
Symmetry, shifts and periodicity
Addition theorems, sum and difference identities of two functions
Products of two functions
Power reduction formula
Multiple-angle formulæ
Half-angle formulæ
Inverse trigonometric functions
- Definition of the inverse trigonometric functions
- Relationships between trigonometric functions and inverse trigonometric functions
- Relationships among the inverse trigonometric functions
Power series expansions, infinite product formulæ
Relationship to the complex exponential function

Keywords:
trigonometric, functions, sine, cosine, tangent, secant, cosecant, versin, vercosin, coversin, covercosin, haversin, havercosin, hacoversin, hacovercosin, exsec, excsc, crd, sinc, cis, inverse, complex, exponential, power, series, expansion, euler, identity, pythagorean

Downloads:

M005: Astrodynamical Constants

A listing of commonly used constants in astrodynamics as well as in space science and engineering with their latest values according to recent publications. This Memorandum is going to be updated with new constants from time to time.

Downloads: