Hamiltonian mechanics is a mathematical formalism used to describe the motion of classical systems in physics. It is named after [[William Rowan Hamilton]], who developed the theory in the 19th century. In Hamiltonian mechanics, the state of a physical system is described by its position and momentum at a given time. These variables are collectively known as generalized coordinates and generalized momenta. The Hamiltonian of the system, denoted by H, is a function that represents the total energy of the system. The equations of motion in Hamiltonian mechanics are derived from Hamilton's equations, which relate the time derivatives of position and momentum to partial derivatives of the Hamiltonian. These equations can be used to determine how a system evolves over time. One key concept in Hamiltonian mechanics is phase space, which is a higher-dimensional space where each point represents a possible state of the system. The evolution of the system can be visualized as a trajectory or path through this phase space. Hamiltonian mechanics has applications in various branches of physics, such as celestial mechanics, quantum mechanics, and statistical mechanics. It provides a powerful framework for analyzing and predicting the behavior of physical systems with multiple degrees of freedom. # References ```dataview Table title as Title, authors as Authors where contains(subject, "Hamiltonian mechanics") or contains(subject, "Hamiltonian") or contains(subject, "Lagrangian") or contains(subject, "Energy Accounting") ```