Suntay and Euler – is there a difference?
First, purists make a distinction between Euler angles and Cardanic angles. Euler rotations are XYX, XZX, YXY, YZY, ZXZ, ZYZ, i.e. all six sequences where the first and last rotation are about the same coordinate axis. These were originally developed for celestial mechanics, i.e. the first rotation would be the orbit, the last the spin, and the second the tilt of the axis. These have a singularity when the second rotation is zero. Cardanic representations are XYZ, XZY, YZX, YXZ, ZXY, ZYX. These six sequences have a singularity (Gimbal lock) when the second rotation is 90 degrees. All of these (Euler and Cardan angles) are now loosely referred to as “Euler angles”. In mechanics textbooks you usually still find the distinction. Yes, they are the same as Grood/Suntay. The matrix representation is exactly the same. Grood really confused the issue by insisting that this was not a sequence of rotations, but three simultaneous rotations. But by arranging the mechanical linkage in a certain wa
