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Hello everyone,
Could anybody tell me, informally, how to plot the construction of an involute curve without involving arclengths (or just give me an efficient way of drawing an involute curve for "any" given parametric curve).
I'm trying to draw the involute of the curve described parametrically by , but then I have to integrate which is just unwieldy and slows down the calculations to no end (as I have to calculate it at each step) (the Wolfram integrator returns a function with about 50 sines/cosines).
The method I'm using now uses the equation on the involute page : describes the equation of the involute when using arclength parametrization, but here I can't use arclength parametrization, nor can I use the other equations which need the evaluation of the arclength.
I'm not too willing to start coding implementations of algorithms for numeric calculation of arclengths eiter, I haven't really got the time.
Anyway, thanks to everyone that can help out. -- Xedi ( talk) 04:51, 4 January 2008 (UTC)
This is the mess I get :
Integrate[ (((2.4*Cos[4*x] - 2.4*Cos[x])^2 + (2.4*Sin[4*x] - 2.4*Sin[x]))^2)^ (1/2), x] ==
(0.*Sqrt[((2.4*Cos[x] - 2.4*Cos[4*x])^ 2 - 2.4*Sin[x] + 2.4*Sin[4*x])^ 2])/((2.4*Cos[x] - 2.4*Cos[4*x])^ 2 - 2.4*Sin[x] + 2.4*Sin[4*x]) + (5.76x* Sqrt[((2.4*Cos[x] - 2.4*Cos[4*x])^ 2 - 2.4*Sin[x] + 2.4*Sin[4*x])^ 2])/((2.4*Cos[x] - 2.4*Cos[4*x])^ 2 - 2.4*Sin[x] + 2.4*Sin[4*x]) + (2.4*Cos[x]*Sqrt[ ((2.4*Cos[x] - 2.4*Cos[4*x])^2 - 2.4*Sin[x] + 2.4*Sin[4*x])^2])/ ((2.4*Cos[x] - 2.4*Cos[4*x])^2 - 2.4*Sin[x] + 2.4*Sin[4*x]) - (0.6*Cos[4.*x]* Sqrt[((2.4*Cos[x] - 2.4*Cos[4*x])^ 2 - 2.4*Sin[x] + 2.4*Sin[4*x])^ 2])/((2.4*Cos[x] - 2.4*Cos[4*x])^ 2 - 2.4*Sin[x] + 2.4*Sin[4*x]) + (1.44*Sin[2.*x]* Sqrt[((2.4*Cos[x] - 2.4*Cos[4*x])^ 2 - 2.4*Sin[x] + 2.4*Sin[4*x])^ 2])/((2.4*Cos[x] - 2.4*Cos[4*x])^ 2 - 2.4*Sin[x] + 2.4*Sin[4*x]) - (1.92*Sin[3.*x]* Sqrt[((2.4*Cos[x] - 2.4*Cos[4*x])^ 2 - 2.4*Sin[x] + 2.4*Sin[4*x])^ 2])/((2.4*Cos[x] - 2.4*Cos[4*x])^ 2 - 2.4*Sin[x] + 2.4*Sin[4*x]) - (1.152*Sqrt[ ((2.4*Cos[x] - 2.4*Cos[4*x])^2 - 2.4*Sin[x] + 2.4*Sin[4*x])^2]* Sin[5.*x])/ ((2.4*Cos[x] - 2.4*Cos[4*x])^2 - 2.4*Sin[x] + 2.4*Sin[4*x]) + (0.36* Sqrt[((2.4*Cos[x] - 2.4*Cos[4*x])^ 2 - 2.4*Sin[x] + 2.4*Sin[4*x])^ 2]*Sin[8.*x])/ ((2.4*Cos[x] - 2.4*Cos[4*x])^2 - 2.4*Sin[x] + 2.4*Sin[4*x])
I think this reformulated function overcomes the problems you have pointed out. Pallida Mors 18:36, 4 January 2008 (UTC)
give some examples of fuzzy logic problems in electrical field?10:21, 4 January 2008 (UTC)
saw this [1]
and wondered if anyone knew of any good freeware for entering LaTeχ into Microsoft office. Thanks! 172.200.130.39 ( talk) 15:20, 4 January 2008 (UTC)
also is it true to say that —Preceding unsigned comment added by 172.200.130.39 ( talk) 16:28, 4 January 2008 (UTC)
Mathematics desk | ||
---|---|---|
< January 3 | << Dec | January | Feb >> | January 5 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
Hello everyone,
Could anybody tell me, informally, how to plot the construction of an involute curve without involving arclengths (or just give me an efficient way of drawing an involute curve for "any" given parametric curve).
I'm trying to draw the involute of the curve described parametrically by , but then I have to integrate which is just unwieldy and slows down the calculations to no end (as I have to calculate it at each step) (the Wolfram integrator returns a function with about 50 sines/cosines).
The method I'm using now uses the equation on the involute page : describes the equation of the involute when using arclength parametrization, but here I can't use arclength parametrization, nor can I use the other equations which need the evaluation of the arclength.
I'm not too willing to start coding implementations of algorithms for numeric calculation of arclengths eiter, I haven't really got the time.
Anyway, thanks to everyone that can help out. -- Xedi ( talk) 04:51, 4 January 2008 (UTC)
This is the mess I get :
Integrate[ (((2.4*Cos[4*x] - 2.4*Cos[x])^2 + (2.4*Sin[4*x] - 2.4*Sin[x]))^2)^ (1/2), x] ==
(0.*Sqrt[((2.4*Cos[x] - 2.4*Cos[4*x])^ 2 - 2.4*Sin[x] + 2.4*Sin[4*x])^ 2])/((2.4*Cos[x] - 2.4*Cos[4*x])^ 2 - 2.4*Sin[x] + 2.4*Sin[4*x]) + (5.76x* Sqrt[((2.4*Cos[x] - 2.4*Cos[4*x])^ 2 - 2.4*Sin[x] + 2.4*Sin[4*x])^ 2])/((2.4*Cos[x] - 2.4*Cos[4*x])^ 2 - 2.4*Sin[x] + 2.4*Sin[4*x]) + (2.4*Cos[x]*Sqrt[ ((2.4*Cos[x] - 2.4*Cos[4*x])^2 - 2.4*Sin[x] + 2.4*Sin[4*x])^2])/ ((2.4*Cos[x] - 2.4*Cos[4*x])^2 - 2.4*Sin[x] + 2.4*Sin[4*x]) - (0.6*Cos[4.*x]* Sqrt[((2.4*Cos[x] - 2.4*Cos[4*x])^ 2 - 2.4*Sin[x] + 2.4*Sin[4*x])^ 2])/((2.4*Cos[x] - 2.4*Cos[4*x])^ 2 - 2.4*Sin[x] + 2.4*Sin[4*x]) + (1.44*Sin[2.*x]* Sqrt[((2.4*Cos[x] - 2.4*Cos[4*x])^ 2 - 2.4*Sin[x] + 2.4*Sin[4*x])^ 2])/((2.4*Cos[x] - 2.4*Cos[4*x])^ 2 - 2.4*Sin[x] + 2.4*Sin[4*x]) - (1.92*Sin[3.*x]* Sqrt[((2.4*Cos[x] - 2.4*Cos[4*x])^ 2 - 2.4*Sin[x] + 2.4*Sin[4*x])^ 2])/((2.4*Cos[x] - 2.4*Cos[4*x])^ 2 - 2.4*Sin[x] + 2.4*Sin[4*x]) - (1.152*Sqrt[ ((2.4*Cos[x] - 2.4*Cos[4*x])^2 - 2.4*Sin[x] + 2.4*Sin[4*x])^2]* Sin[5.*x])/ ((2.4*Cos[x] - 2.4*Cos[4*x])^2 - 2.4*Sin[x] + 2.4*Sin[4*x]) + (0.36* Sqrt[((2.4*Cos[x] - 2.4*Cos[4*x])^ 2 - 2.4*Sin[x] + 2.4*Sin[4*x])^ 2]*Sin[8.*x])/ ((2.4*Cos[x] - 2.4*Cos[4*x])^2 - 2.4*Sin[x] + 2.4*Sin[4*x])
I think this reformulated function overcomes the problems you have pointed out. Pallida Mors 18:36, 4 January 2008 (UTC)
give some examples of fuzzy logic problems in electrical field?10:21, 4 January 2008 (UTC)
saw this [1]
and wondered if anyone knew of any good freeware for entering LaTeχ into Microsoft office. Thanks! 172.200.130.39 ( talk) 15:20, 4 January 2008 (UTC)
also is it true to say that —Preceding unsigned comment added by 172.200.130.39 ( talk) 16:28, 4 January 2008 (UTC)