Periodic motion refers to the repeated back-and-forth movement of an object or system over a fixed period of time, creating a cycle that can be described mathematically. This type of motion is characterized by its regularity and can be found in various physical systems, such as pendulums, springs, and planetary orbits. Understanding periodic motion is essential for analyzing dynamic systems, especially in the context of Hamilton-Jacobi theory and action-angle variables, where it plays a key role in simplifying complex motion into more manageable forms.
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