# Fp3 CurvatureWatch

Thread starter 12 years ago
#1
Hiya,

Just got going on some curvature questions, the first ones were fine, but I've become stuck on this question, on both parts. Can someone please explain it? Thanks

Find the curvature of the astroid:
(i) using the intrinsic equation s=1.5a * (sinx)^2 [or in this form 1.5a(sin^2)x]

(ii) using the parametric equations x=a((cosp)^3), y=a((sinp)^3)

Thanks
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Thread starter 12 years ago
#2
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Thread starter 12 years ago
#3
anybody? , last bump by the way.
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12 years ago
#4
(Original post by dholmes_7)
Hiya,

Just got going on some curvature questions, the first ones were fine, but I've become stuck on this question, on both parts. Can someone please explain it? Thanks

Find the curvature of the astroid:
(i) using the intrinsic equation s=1.5a * (sinx)^2 [or in this form 1.5a(sin^2)x]

(ii) using the parametric equations x=a((cosp)^3), y=a((sinp)^3)

Thanks
Im assuming that it a Psi in part (i) and not x ??

mrm.
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Thread starter 12 years ago
#5
(Original post by Mrm.)
Im assuming that it a Psi in part (i) and not x ??

mrm.
Yes, it was just easier to put x, but yes its psi
0
12 years ago
#6
(Original post by dholmes_7)
Yes, it was just easier to put x, but yes its psi

well the radius of curvature is just ds by d (psi)

so from s=1.5a * (sin(psi))^2

r.of c. = 2 x 1.5a x sin (psi) cos(psi)

= 1.5a sin (2psi)

for the second one just use

( x dot ^2 + y dot ^2) ^(3/2) over (x dot y dot dot - y dot x dot dot)

If you are unsure / or want to see where the formula comes from then I'll jot it down tommorrow,

mrm.
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