Action Integral

The action integral is a concept from physics and calculus used to analyze the behavior of systems, like planets or particles, over time. It involves calculating a quantity called "action" by integrating (adding up) the difference between kinetic energy (motion) and potential energy (position or configuration) along a path or trajectory. The principle of least action states that systems naturally follow the path that minimizes this action. This approach provides a powerful way to predict how objects move and how systems evolve, offering a unified framework that connects various physical laws through a mathematical lens.