Consider a rocket with an axis of symmetry. The mass of the rocket is 1 kg. The rocket takes off from a launch pad with zero translational velocity and an initial spin rate of 0.85 rad/sec about the axis of symmetry. The thrust acts at the rear nozzle with a 2.5-degree misalignment from the axis of symmetry. The thrust magnitude is 15 N and acts for 10 sec. Gravity acts in the vertical plane and the gravitational constant is taken to be 9.81 m/sec2. The inertia tensor of the rocket coordinatized in a principal frame located at the mass center is P [Ic] = diag [ 32.5 32.5 5 ] kg-m2. The distance from the mass center to the rear nozzle is 3 m along the axis of symmetry whereas the distance from the mass center to the nose is 4 m along the axis of symmetry. Let the attitude of the principal frame relative to an inertial frame be parameterized using (1-2-3) Euler angle sequence through the angles (α, β, γ). Simulate the motion of the rocket for 60 sec. Plot the principal frame components of the rocket’s translational velocity vector.

Consider a rocket with an axis of symmetry. The mass of the rocket is 1 kg. The rocket takes off from a launch pad with zero translational velocity and an initial spin rate of 0.85 rad/sec about the axis of symmetry. The thrust acts at the rear nozzle with a 2.5-degree misalignment from the axis of symmetry. The thrust magnitude is 15 N and acts for 10 sec. Gravity acts in the vertical plane and the gravitational constant is taken to be 9.81 m/sec2. The inertia tensor of the rocket coordinatized in a principal frame located at the mass center is P [Ic] = diag [ 32.5 32.5 5 ] kg-m2. The distance from the mass center to the rear nozzle is 3 m along the axis of symmetry whereas the distance from the mass center to the nose is 4 m along the axis of symmetry. Let the attitude of the principal frame relative to an inertial frame be parameterized using (1-2-3) Euler angle sequence through the angles (α, β, γ). Simulate the motion of the rocket for 60 sec. Plot the principal frame components of the rocket’s translational velocity vector.