1. There is a spacecraft in the form of a ball of radius R and mass M, uniformly distributed over the volume. We investigate the rotation around an axis passing through the center of the spacecraft such that a set of engines with masses m1, m2, m3 lies in the plane of rotation. Each engine can give angular acceleration eps_i. The initial rotation speed w is given.

a) Investigate different variants of angular accelerations for one motor (constant, variable). Solve the basic equation of rigid body dynamics, see if the rotational velocity can be zeroed out.

(b) Investigate different arrangements of orientation control motors (one, two, three, different angles between them). Investigate the issue of the fastest settling of rotation - just parametrically set the angular accelerations and see if the time in which the velocity is zeroed out decreases.

2. There is a spacecraft in the form of a cylinder of length L and radius R, combined with a cone of base radius R and height h (similar to Apollo). The mass of the cylinder is M1, the mass of the cone is M2, each mass is evenly distributed over the volume. The rotation occurs around the axis passing through the longitudinal axes of the cylinder and cone. The initial velocity of rotation w is set. Similarly to point 1, calm the rotation. The location of the orientation control motors and the form of angular accelerations are at the student's discretion. It will be necessary to independently write out the moment of inertia of the spacecraft relative to the longitudinal axis. It is desirable to give as much as possible the opportunity to adjust the parameters of the problem.

p.s.
You may write program in Python or use Mathcad/Matlab.