I am a bit confused about the difference between direction cosine matrix(DCM) and rotation matrix. I have searched through the literature but found no explicit explanation if they are different or same and when should each of them be used. For DCM I have referred to this documents ([DCM][1]) and what I understood is that the DCM and rotation matrix for a Yaw,Pitch,Roll sequence can be calculated as shown in the code snippet below:
import math
import numpy as np
yaw = np.deg2rad(90);
pitch = np.deg2rad(0);
roll = np.deg2rad(0);
yawMatrix = np.matrix([[math.cos(yaw), -math.sin(yaw), 0], [math.sin(yaw), math.cos(yaw), 0], [0, 0, 1] ])
pitchMatrix = np.matrix([[math.cos(pitch), 0, math.sin(pitch)], [0, 1, 0], [-math.sin(pitch), 0, math.cos(pitch)] ])
rollMatrix = np.matrix([[1, 0, 0], [0, math.cos(roll), -math.sin(roll)], [0, math.sin(roll), math.cos(roll)] ])
R = yawMatrix * pitchMatrix * rollMatrix
dcm_yaw = np.matrix([[math.cos(yaw), math.sin(yaw), 0], [-math.sin(yaw), math.cos(yaw), 0], [0, 0, 1] ])
dcm_pitch = np.matrix([[math.cos(pitch), 0, -math.sin(pitch)], [0, 1, 0], [math.sin(pitch), 0, math.cos(pitch)] ])
dcm_roll = np.matrix([[1, 0, 0], [0, math.cos(roll), math.sin(roll)], [0, -math.sin(roll), math.cos(roll)] ])
DCM = dcm_yaw * dcm_pitch * dcm_roll
print(R)
print(DCM) Is this intepretation of DCM and rotation matrices correct? [1]:
$\endgroup$1 Answer
$\begingroup$Yes DCM is a rotation matrix.
You can check it is defined as rotation matrix in this paper of the "MEMS inertial navigation systems for aircraft"
And in several other papers is regarded as member of SO(3) group, which means it is a rotation. Also, you can check the matrix is orthogonal and its determinant is equal to one, which is the dedinition of a rotation matrix.
$\endgroup$
