Thank for your answer. Please, if it is possible, can you recommend me some books/papers? OK, it seems to be Leibniz rule, but why it was used ##\delta r## instead of ##\dot{r}##... I have the feeling that something is missing me.
I have a paper and on that paper I only can read:
Let $$f:\mathbb{S^{1}} \to \mathbb{R^2}$$ be a function and $$f_{\epsilon}=f+\epsilon hn$$ and $$\mathbb{S^1}$$ is the unit circle.
$$\dot{f_\epsilon}=\dot{f}+\epsilon\dot{h}n+\epsilon h\dot{n}$$
$$\delta\dot{f}=\dot{h}n+h\dot{n}$$
can you...