Fp3 Curvature Watch

dholmes_7
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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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dholmes_7
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Please help someone!
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dholmes_7
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anybody? , last bump by the way.
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Trevor 12345
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(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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dholmes_7
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(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
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Trevor 12345
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(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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