Normal coordinates are a fundamental concept in mathematics and physics, referring to a set of coordinates in which the equations of motion for a particular system are easiest to solve. There are several synonyms for the term "normal coordinate," including canonical coordinates, phase coordinates, and generalized coordinates. These terms refer to different aspects of the normal coordinate system, with canonical coordinates emphasizing the symplectic structure of the system, phase coordinates emphasizing the periodicity inherent in many systems, and generalized coordinates emphasizing the flexibility of the normal coordinate system to describe a wide range of possible physical systems. No matter which term one prefers, the concept of normal coordinates remains essential for understanding complex mathematical and physical systems.