Generalized Coordinates

Generalized coordinates are a set of parameters used to describe the position and movement of a system in a way that simplifies analyzing complex motion. Unlike standard coordinates (like x, y, z), they are chosen to match the system’s constraints and natural motions, reducing the number of variables needed. For example, a swinging pendulum can be described by just one angle instead of multiple measurements. This approach makes it easier to understand and compute how systems move, especially when dealing with multiple interconnected parts, by focusing on the most relevant degrees of freedom.