- #1
egozenovius
- 2
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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 tell me please, what does it mean that $$\delta$$, from where is it? Why $$\dot{f}$$ is not anymore in last equation?
also, I managed to recover the following formula:
$$r_{\epsilon}^{2}=\left(\dot{f}+\epsilon\dot{h}n+\epsilon h\dot{n}\right)^2$$
Can you help me to recover the $$\delta{r}$$?
What I tried:
$$r_{\epsilon}^2=(\dot{f})^2+(\epsilon \dot{h}n)^2+(\epsilon h\dot{n})^2+2(\dot{f}\epsilon\dot{h}n+\dot{f}\epsilon h\dot{n}+\epsilon^2\dot{h}nh\dot{n})$$
But now, I do not know how to compute $$\delta r$$.
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 tell me please, what does it mean that $$\delta$$, from where is it? Why $$\dot{f}$$ is not anymore in last equation?
also, I managed to recover the following formula:
$$r_{\epsilon}^{2}=\left(\dot{f}+\epsilon\dot{h}n+\epsilon h\dot{n}\right)^2$$
Can you help me to recover the $$\delta{r}$$?
What I tried:
$$r_{\epsilon}^2=(\dot{f})^2+(\epsilon \dot{h}n)^2+(\epsilon h\dot{n})^2+2(\dot{f}\epsilon\dot{h}n+\dot{f}\epsilon h\dot{n}+\epsilon^2\dot{h}nh\dot{n})$$
But now, I do not know how to compute $$\delta r$$.