Hamiltonian system

A Hamiltonian system is a type of equation used in physics to describe the motion of a system. It describes how the position and momentum of a system change over time. To understand this, we can think about a simple example of a ball rolling along a hill.

The Hamiltonian equation tells us how the ball's position is related to its momentum (how fast it is going) and tells us how the momentum is related to the forces acting on the ball, such as gravity. This helps us understand how the ball will move over time and how it will respond if something changes in the environment.