Give a top a spin and the top does not fall. Instead it turns about the vertical at a steady rate, and the faster it is spinning the slower it precesses. The reason is that gravity is trying to make the top fall, and the only way the top can fall is by turning about its own axis — and it is already turning about its own axis, very fast, so the fall becomes a sideways sweep instead.
For a symmetric top there are three Euler angles: the tilt θ from the vertical, the precession φ about the vertical, and the spin ψ about the top's own axis. Gravity applies no torque about the symmetry axis, so the angular momentum along that axis is constant, and because the pivot is fixed, the angular momentum about the vertical is constant too.
Those two conserved quantities, together with the energy, give the closed-form precession rate: φ̇ = (pφ − pψ cos θ) / (A sin² θ). Put in a fast spin and the numerator grows, so the precession slows. That is the whole of the gyroscope, and it is why a spinning wheel does not fall over.