aviation
general 3d rotation matrix
R = R_z(𝛼) R_y(β) R_x(𝛾) matrix multiplication is not commutative so order matters
yaw matrix
R_z(𝛼) = {{cos 𝛼, -sin 𝛼, 0}, {sin 𝛼, cos 𝛼, 0}, {0, 0, 1}}
pitch matrix
R_y(β) = {{cos β, 0, sin β}, {0, 1, 0}, {-sin β, 0, cos β}}
Yaw, pitch, and roll
Yaw --- flatspin; use rudder to control. Pitch --- backflip; use elevator to control. Roll --- barrel roll; use ailerons to control.
roll matrix
R_x(𝛾) = {{1, 0, 0}, {0, cos 𝛾, -sin 𝛾}, {0, sin 𝛾, cos 𝛾}}