Show that the angular velocity of a body, in terms of Euler angles ϕ, θ, and ψ, can be exp...

Show that the angular velocity of a body, in terms of Euler angles ϕ, θ, and ψ, can be expressed as ω = (ϕ sin θ sin ψ + θ cos ψ)i + sin θ cos ψ − θ sin ψ)j + (ϕ cos θ + ψ)k, where i, j, and k are directed along the x, y, z axes as shown in Fig.