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January 20th, 2015, 07:25 PM   #1
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Any special case satisfying $\arctan{\frac{dy(c+s)} {dx(c+s)}}$

There is a mysterious parametric curve:
$$ x(s),y(s)$$
defined on three intervals (continuity unkown) around a, b, and c $(a< b\leq c)$, thus the curve consists of three segments :
$$x(a+s) ,y(a+s)$$
$$x(b-s) ,y(b-s)$$
$$x(c+s) ,y(c+s)$$
that satisfy the following equations:
$$\frac{dy(c+s)}{dx(c+s)}=\frac{y(c+s)-y(b-s)}{x(c+s)-x(b-s)}$$
$$\frac{dy(a+s)}{dx(a+s)}=\frac{y(a+s)-y(b-s)}{x(a+s)-x(b-s)}$$
$$\arctan{\frac{dy(c+s)} {dx(c+s)}}-\arctan{\frac{dy(a+s)} {dx(a+s)}}=\pi-\theta$$
here:
$$\frac{dy(c+s)/ds}{dx(c+s)/ds}=\frac{dy(c+s)}{dx(c+s)}$$
I guess the conditions above are not sufficient to work out $x(s), y(s)$ , however, is it possible to give any special case satisfying above equations? Now I have no clue how to go any further on this problem.Thanks for any suggestions.
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January 21st, 2015, 06:37 AM   #2
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What do you mean by "dy(c+s)"?
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January 21st, 2015, 06:01 PM   #3
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Quote:
Originally Posted by Country Boy View Post
What do you mean by "dy(c+s)"?
dy(c+s) means d(y(c+s)) the infinitesimal change in y(as a function of s), c is a constant.
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