Hamiltonian Dynamics is a framework in classical mechanics that describes the evolution of a physical system over time. It is based on the principle of energy conservation and uses a set of equations derived from a function called the Hamiltonian, which represents the total energy of the system. This approach allows for a clear understanding of how systems change and interact. In Hamiltonian Dynamics, the state of a system is represented by generalized coordinates and momenta. The equations of motion, known as Hamilton's equations, provide a systematic way to analyze complex systems, making it easier to study phenomena in various fields, including physics, engineering, and mathematics.