Hamiltonian Dynamics

Hamiltonian dynamics is a framework in physics used to describe how systems evolve over time, especially in classical mechanics. It uses a function called the Hamiltonian, typically representing the total energy (kinetic + potential) of the system, expressed in terms of positions and momenta (motion-related variables). By applying specific equations, the Hamiltonian tells us how the positions and momenta change over time. This approach provides a powerful and elegant way to analyze complex systems like planets or particles, offering deep insights into their behavior through a unifying mathematical structure.