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Allamarein
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 Posted: Sat Nov 01, 2008 11:54 am Post subject: Radius of curvature |
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Let>s suppose to have a reference system X-Y.
I have a curve with its own curvilinear abscissa "s". I have the
"alpha" function alpha(s), that is the angle between X and s-versor
for each s.
What is it the radius of curvature at each "s"? I>d need the function
"radius of curvature" R(s)
Allamarein |
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Anders
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| Posted: Sun Nov 02, 2008 3:57 pm Post subject: Re: Radius of curvature |
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On Nov 1, 12:54 pm, Allamarein <matteo.diplom...@gmail.com> wrote:
[quote]Let>s suppose to have a reference system X-Y.
I have a curve with its own curvilinear abscissa "s". I have the
"alpha" function alpha(s), that is the angle between X and s-versor
for each s.
What is it the radius of curvature at each "s"? I>d need the function
"radius of curvature" R(s)
Allamarein
[/quote]
The derivative of the function alpha w.r.t. s.
D (alpha) (s)
HTH
Anders |
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Allamarein
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| Posted: Mon Nov 03, 2008 12:33 am Post subject: Re: Radius of curvature |
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On 2 Nov, 16:57, Anders <Anders.Lyckega...@gmail.com> wrote:
[quote]On Nov 1, 12:54 pm, Allamarein <matteo.diplom...@gmail.com> wrote:
Let>s suppose to have a reference system X-Y.
I have a curve with its own curvilinear abscissa "s". I have the
"alpha" function alpha(s), that is the angle between X and s-versor
for each s.
What is it the radius of curvature at each "s"? I>d need the function
"radius of curvature" R(s)
Allamarein
The derivative of the function alpha w.r.t. s.
D (alpha) (s)
HTH
Anders
[/quote]
Ok..I supposed that.
Now I know the function alpha(s). How can I can describe my curve in X-
Y plane?
That is I have n "s" value, hence I have n "alpha" value (or,if you
prefer, I know the alpha=alpha(s) function)
How can report these positions in X-Y plane?
I mean to know the n X-Y pairs. (or to know the y=y(x) function from
alpha(s) function)
Let>s suppose that our starting point is (0,0).
I think that the "i" position should be:
X(i)=X(i-1)+(s(i)-s(i-1))*cos(alpha(i))
Y(i)=Y(i-1)+(s(i)-s(i-1))*sin(alpha(i))
with X(0)=Y(0)=s(0)=0 in this case
Am I right? |
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