Attitude Representation

Quaternion Gibbs Vector / Rodrigues Parameter Representation Modified Rodrigues Parameters Cayley-Klein References: Gibbs Vector / Rodrigues Parameter Representation The Gibbs vector also known as Rodrigues Parameter is a set of three parameters denoted by $ g $ (or $ P $) and can be directly derived from axis-angle $ (e, \theta) $ or quaternion representation as follows:

Euler Angles Euler Parameters (Quaternions) representation References: Euler Parameters (Quaternions) representation A four-element vector with three imaginary and one real component is known as Quaternion. These hypercomplex numbers are optimum for numerical stability and memory load.

Attitude Representation Euler Angles Representation References: Euler Angles Representation A vector of three angles that represent the attitude of the coordinate frame $ i $ with respect to the coordinate frame $ j $ is called Euler angles.

Direction Cosine Matrix (DCM) Axis-Angle Representation References: Attitude Attitude representation is a set of coordinates that fully describe a rigid body’s orientation with respect to a reference frame. There are an infinite number of attitude representations, each of which has strengths and weaknesses.