Kovaleskaya's Spinning Top or The Best Way to Spin

How do you model the movement of a potato in space? Many a mathematician has struggled with this question. At the end of the 19th century, mathematician Sofia Kovalevskaya finally obtained an important result for determining the motion of a solid around a fixed point, thanks to a very special spinning top. A little expedition to the heart of integrable systems, even if it's a bit dizzying...