1. The inertia matrix of an object is given by J1 2 1 (a) Find the principal moments of inertia and the principal axes of rotation for this object by hand. Check your answers in MATLAB (b) Derive by hand, the rotational equations of motion in the principal axes frame. (c) Using ODE45 in MATLAB simulate this system for an initial angular velocity of 2 rads/s in the first principal axis (i direction,p-frame) and no torque input, for 10 seconds. Be sure to use the eigenvalues as provided by MATLAB. That is X1 should be the first eigenvalue out of eig() in MATLAB and ect. Please attach the code. Use publish in Matlab for the codes and plots (d) Using ODE45 in MATLAB simulate this system for initial angular velocities of 2 rads/s in the first principal axis and torque input of 1 unit about the first principal axis, for 10 seconds. Provide a plot of results (e) Using ODE45 in MATLAB simulate this system for initial angular velocities of 0 rads/s and torque input of 1 unit about the second and third principal axis, for 10 seconds. Provide a plot of results (f) Based on the results of (c), (d), and (e) what can you say about torques and angular velocities about principal axes of rotation. (g) Using ODEA5 in MATLAB simulate this system for initial angular velocities of 0 rads/s in the first principal axis and torque input of cos(t) + 8sin(2t) in the first principal axis, for 10 seconds. Provide a plot of results 1. The inertia matrix of an object is given by J1 2 1 (a) Find the principal moments of inertia and the principal axes of rotation for this object by hand. Check your answers in MATLAB (b) Derive by hand, the rotational equations of motion in the principal axes frame. (c) Using ODE45 in MATLAB simulate this system for an initial angular velocity of 2 rads/s in the first principal axis (i direction,p-frame) and no torque input, for 10 seconds. Be sure to use the eigenvalues as provided by MATLAB. That is X1 should be the first eigenvalue out of eig() in MATLAB and ect. Please attach the code. Use publish in Matlab for the codes and plots (d) Using ODE45 in MATLAB simulate this system for initial angular velocities of 2 rads/s in the first principal axis and torque input of 1 unit about the first principal axis, for 10 seconds. Provide a plot of results (e) Using ODE45 in MATLAB simulate this system for initial angular velocities of 0 rads/s and torque input of 1 unit about the second and third principal axis, for 10 seconds. Provide a plot of results (f) Based on the results of (c), (d), and (e) what can you say about torques and angular velocities about principal axes of rotation. (g) Using ODEA5 in MATLAB simulate this system for initial angular velocities of 0 rads/s in the first principal axis and torque input of cos(t) + 8sin(2t) in the first principal axis, for 10 seconds. Provide a plot of results