Standard Notation

Standard notation developed in the first three chapters and used throughout the remainder of this book is given below. Unfortunately, notation, coordinate systems, and even definitions are frequently used differently for different spacecraft. The definition of attitude and the orientation of the roll, pitch, and yaw axes vary more than most quantities.

Alphabets and Type Styles

All arc lengths are lowercase Greek, 0 All rotation angles are uppercase Greek, A

These are not exclusive because common usage may require Greek characters for some nonangular measure.

All «-vectors are bold face, E or x. All quaternions are boldface italics, q. Boldface is used exclusively for vectors, quaternions, or the identity matrix, 1.

Points on the sky are labeled with uppercase italic Roman, E. Antipodal points (the antipode is the point 180 deg away from a given point) have a - 1 superscript, E~l.

Vectors and Matrices

The treatment of vectors is illustrated by the Sun vector:

S point on the celestial sphere in the direction of the Sun

S-1 point on the celestial sphere opposite the direction of the Sun

S vector from spacecraft to Sun

S unit vector from the spacecraft toward the Sun

|S| or 5 magnitude of the Sun vector. S is used if there is no possibility of ambiguity. Otherwise |S| is used S, either the ith component of the Sun vector or an arbitrary component of the Sun vector

Both uppercase and lowercase letters will be used for vectors. Matrices will be represented by uppercase Roman letters with the following notation:

M or [Mi}\ matrix or second-rank tensor det M or \M(J\ determinant of M

M ~1 inverse of M

Mt transpose of M

Mij either an arbitrary component of M or the component in the ith row, yth column

1 identity matrix

I moment of inertia tensor

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