A uniform top of mass $M$ with its lower end fixed to the ground is rotating on its axis of symmetry with angular velocity $\Omega$, initially in a vertical position ($\theta=0, \dot \theta=0$). The main moments of inertia are $I_3,I_1=I_2$. The center of mass is located at a distance $a$ from the bottom point of the top. I need to find the quantities conserved in the system based on the initial conditions and calculate the maximum angle that the top can be tilted.
I tried to solve the problem without initial conditions (Lagrange Top) and obtaining the conserved quantities from the Lagrangian, which I have left in terms of Euler's angles, but now I don't know when to use the initial conditions, if it is from the start in the problem statement or once you have the Lagrangian just substitute the initial condition values?