Chapter 21.4, Problem 60P

Show that the angular velocity of a body, in terms of Euler· angles ϕ, θ, and ψ, can be expressed as ω = ( $\stackrel{\dot{}}{\varphi }$sin θ sin ψ + $\stackrel{\dot{}}{\theta }$cos ψ)i + ( $\stackrel{\dot{}}{\varphi }$sin θ cos ψ – $\stackrel{\dot{}}{\theta }$ sin ψ)j + ( $\stackrel{\dot{}}{\varphi }$ cos θ + $\stackrel{\dot{}}{\psi }$)k, whore i, j, and k are directed along the x, y, z axes as shown Fig. 21-15d.