In classical mechanics, the behavior of a system can be described using the principle of _____, which states that the path taken by a system is the one that minimizes the action integral.

The principle is called the principle of least action, also known as Hamilton's principle. It says that when a system moves from one point to another, it chooses the path that makes the action integral as small as possible. The action integral is the time integral of the Lagrangian, which is kinetic energy minus potential energy, and it measures how the system’s energy changes over time. For example, a thrown ball follows a curved arc because that trajectory makes the action integral minimal compared to any other possible path. This idea underlies many predictions in physics, from planetary orbits to quantum mechanics.