What is the general mathematical definition of periodic motion?

What is the general mathematical definition of periodic motion?

My answer : Can you say that each function is in the form $$\overrightarrow{r} (t)= \overrightarrow{r} (t+T)$$.

it is right?

• – Kyle Kanos Nov 13 '18 at 17:25
• Note that this definition would preclude something like (under) damped harmonic motion to be included in the definition of "periodic motion". – enumaris Nov 13 '18 at 17:28

So to answer your question $$\overrightarrow{r} (t)= \overrightarrow{r} (t+T)$$ describes periodic motion.