Hamiltonian mechanics

Hamiltonian Mechanics is a branch of mathematics that explains how physical systems move over time. It is named after William Rowan Hamilton, an Irish mathematician who first used it to explain the motion of particles and systems. It is used in physics and chemistry to determine the way in which a system will move.

Think of a system as a group of objects interacting with each other. For example, if you put three billiard balls next to each other and strike one of them, the other two will move away due to the energy created by the impact. Hamiltonian Mechanics explains how this energy is transferred between the objects, and how their motion is determined.

In Hamiltonian Mechanics, the objects in the system are described by equations. From these equations, the motion of the system can be worked out. For example, if you want to work out how fast the two billiard balls move after you strike one of them, you could use Hamiltonian Mechanics to work out the answers.

So, in summary, Hamiltonian Mechanics is a way of using math to describe how physical systems move over time. It is used in physics and chemistry to figure out how energy is transferred between objects and how their motion is determined.