Hamiltonian systems

Hamiltonian systems are mathematical frameworks used to describe how physical systems evolve over time, particularly in physics and engineering. Named after the mathematician William Rowan Hamilton, these systems use a function called the Hamiltonian, which represents the total energy of the system. The Hamiltonian helps to derive equations of motion, allowing us to predict how a system, like a planet orbiting a star or a swinging pendulum, changes in response to forces. Hamiltonian mechanics provides a powerful alternative to Newtonian mechanics, particularly in complex systems and advanced areas like quantum mechanics.