Euler Angle Representation and Direction Cosine Matrix Representation for Aircraft Attitude Angles

Aircraft attitude angles refer to their orientation in space, typically represented using Euler angles. Euler angles consist of three components: roll angle, pitch angle, and yaw angle. Direction cosine matrix (DCM) is another method for representing attitude angles - it's a square matrix that defines the aircraft's orientation in three-dimensional space. When converting between Euler angles and direction cosine matrices in MATLAB, specific transformation sequences are implemented using built-in functions. The aerospace toolbox provides essential functions like angle2dcm for converting Euler angles to DCM and dcm2angle for the reverse conversion. These functions implement standard rotation sequences (such as 'ZYX' or 'ZYZ') following aerospace conventions, where each rotation is applied in a specific order around particular axes. The conversion algorithms typically involve constructing individual rotation matrices for each Euler angle and then multiplying them in the correct sequence to form the complete direction cosine matrix.