(a) Consider a particle at position r = (x, y, z) spinning around the axis u...

  

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(a) Consider a particle at position r = (x, y, z) spinning around the axis u where u = angular velocity w. The motion of the particle is given by the equation dr (wu) r dt with initial condition r(0). (i) Write the system as d = Ar. 2 (ii) Find R(w, u,t) = exp(tA) such that r(t) = R(w, u, t) r(0). (iii) Show that R is a rotational matrix and give its axis and angle of rotation. with 3 3. (a) Consider a particle at position r = (x, y, z) spinning around the axis u where u = angular velocity w. The motion of the particle is given by the equation dr (wu) r dt with initial condition r(0). (i) Write the system as d = Ar. 2 (ii) Find R(w, u,t) = exp(tA) such that r(t) = R(w, u, t) r(0). (iii) Show that R is a rotational matrix and give its axis and angle of rotation. with 3 3.