Uploaded August 2021 | Updated September 2026, 4 hours ago
We have seen how Hamiltonian mechanics can be used to solve for the dynamics of physical systems. It turns out that there is quite a bit of hidden power in this formalism in that we can prove some fairly general statements about physics as a whole. We will see one of these results, known as Liouville's theorem, in this stream. We will also introduce the idea of chaos in physics and connect the two by looking at the evolution of chaotic systems in phase space.
We have seen how Hamiltonian mechanics can be used to solve for the dynamics of physical systems. It turns out that there is quite a bit of hidden power in this formalism in that we can prove some fairly general statements about physics as a whole. We will see one of these results, known as Liouville's theorem, in this stream. We will also introduce the idea of chaos in physics and connect the two by looking at the evolution of chaotic systems in phase space.
