Editing Classical Mechanics (section)

== <span style="color: #FFFFFF;">Remembering</span> ==
* '''Lagrangian (L)''' — The difference between Kinetic Energy (T) and Potential Energy (V): $L = T - V$.
* '''Hamiltonian (H)''' — The total energy of a system: $H = T + V$.
* '''Action (S)''' — The integral of the Lagrangian over time; the "Total amount of physical effort" spent by a system.
* '''Principle of Least Action''' — The fundamental law that a system will always follow the path that "Minimizes" the Action.
* '''Euler-Lagrange Equations''' — The "Equations of Motion" derived from the Lagrangian; they replace Newton's F=ma for complex systems.
* '''Phase Space''' — A multi-dimensional "Map" where every point represents a complete "State" (Position and Momentum) of a system.
* '''Noether’s Theorem''' — The "Most beautiful discovery in physics": the proof that every "Symmetry" (e.g., rotating a system doesn't change it) leads to a "Conservation Law" (e.g., Conservation of Angular Momentum).
* '''Generalized Coordinates (q)''' — Using whatever variables are "Natural" for the system (e.g., an "Angle" for a pendulum) instead of just X, Y, and Z.
* '''Canonical Transformations''' — Changing the "Variables" of a system without changing its "Physics," used to simplify hard problems.
* '''Integrability''' — Whether a system's equations can be "Solved perfectly" or if it is "Chaotic."
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