Lecture Notes on Astrometry Rotation (Euclidean) Distance-Invariant Finite Rotation: Matrix representation Orthogonality

Lecture Notes on Astrometry Infinitesimal Rotational Displacement Antisymmetric Matrix Vector Product

Lecture Notes on Astrometry Finite Rotation Expressions: Matrix, Spinol, Quarternion Rotation = Matrix Operation Rot. Matrix = Set of Basis Vectors (= Triad) X Y Z

Lecture Notes on Astrometry Euler ’ s Theorem Any Finite Rotation = 3 Basic Rotation Euler angles: 3 Angles of Basic Rotations

Lecture Notes on Astrometry Basic Rotation Rotation around z-axis by angle q q X Y x y P

Lecture Notes on Astrometry Basic Rotation (contd.) Rotation around j-axis by angle q Inverse Rotation

Lecture Notes on Astrometry Basic Rotation Matrix Example: Equatorial – Ecliptic Obliquity of Ecliptic

Lecture Notes on Astrometry Basic Rotation Matrix (contd.) Small Angle Approximation

Lecture Notes on Astrometry Angular Velocity

Lecture Notes on Astrometry Euler Rotation 3x2x2 = 12 different combinations Sequence (= x-convention) Most popular (Euler angles) Used to describe rotational dynamics

Lecture Notes on Astrometry Euler Angles (3-1-3)

Lecture Notes on Astrometry Euler Angles X Z Y N P y q f

Lecture Notes on Astrometry Demerit of Sequence Degeneration in case of small angles Solution: like Sequences

Lecture Notes on Astrometry Sequence y-convention: precession Conic Rotation Rotation around a fixed direction

Lecture Notes on Astrometry Other Sequences 1-3-1: Nutation 2-1-3: Polar Motion + Sidereal Rotation 1-2-3: Aerodynamics, Attitude Control Best Recommended

Lecture Notes on Astrometry Small Angle Rotation

Lecture Notes on Astrometry Rotational Velocity