{{1, 0, a}, {0, 1, b}, {0, 0, 1}}

Yaw --- flatspin; use rudder to control. Pitch --- backflip; use elevator to control. Roll --- barrel roll; use ailerons to control.

Trans(a, b) Rot(θ) Trans(-a, -b)

R = R_z(𝛼) R_y(β) R_x(𝛾) matrix multiplication is not commutative so order matters

{{ s_x, 0, 0, 0}, { 0, s_y, 0, 0}, {0, 0, s_z, 0}, {0, 0, 0, s_w}}

R_z(𝛼) = {{cos 𝛼, -sin 𝛼, 0}, {sin 𝛼, cos 𝛼, 0}, {0, 0, 1}}

R_y(β) = {{cos β, 0, sin β}, {0, 1, 0}, {-sin β, 0, cos β}}

{{ cos θ, -sin θ, 0}, {sin θ, cos θ, 0}, {0, 0, 1}}

R_x(𝛾) = {{1, 0, 0}, {0, cos 𝛾, -sin 𝛾}, {0, sin 𝛾, cos 𝛾}}