Given a spacecraft with the following principle moments of inertia: [1500 0 0 J = cos(8) 0 1500 0 a) Assuming torque free motion, calculate the minimum rotational velocity n that will keep the nutation angle below 1.0 degree, if the transverse rotational velocity @12 = 0.05 deg/s. (Be careful of units) 0 0 2500 J3n √(W₁2)² + √√√3n)² or tan(0) = b) MATLAB-Given the closed form solutions of the torque free differential equations of motion, use MATLAB to plot how changes over a time period starting at t = 0 seconds to t = 1000 seconds. Use the initial conditions n = 2.0 deg/s, w₁(0) = 0.1 deg/s, w2(0) = 0.6 deg/s. Use the MATLAB function subplot() to create three plots on the same figure for each element of w. w₁(t) = w₁(0) cos(at) + w₂ (0) sin(at) w₂ (t) = w₂(0) cos(at) - w₁(0) sin(at) w3(t) = n Jw12 J3n c) MATLAB - Given the same initial conditions and time period as part (b) and the closed form solutions of the constant torque differential equations of motion, use MATLAB to plot how changes with a constant torque of M₁ = 20.0 Nm. Comment on the similarities and differences between the plots from part (b) and part (c). w₁(t) = w₁(0) cos(lt) + w₂(0) sin(at) + w₂(t) = w₂ (0) cos(lt) — w₁(0) sin(at) - w3(t) = n sin(at) (1 - cos(at))

Inertia can be termed as a resistance offered by a body to change its state. A rigid body initially at rest will apply resistance when acted by an external force that tends to change its state of rest or velocity, or a body initially at motion will provi…