Find The Curvature of the given curve
Find the curvature of the curve :
$ x = t - sin{t} $ , $y = 1 - cos{t} $ , $z=4sin{dfrac{t}{2}}$.
I have been trying to find the curvature using the formula
$ {k_{1}}^2 = dfrac{{begin{vmatrix} x''& y'' \ x' & y' end{vmatrix}}^2 +{begin{vmatrix} y'' & z'' \ y' & z' end{vmatrix}}^2 + {begin{vmatrix} z'' & x'' \ z' & x' end{vmatrix}}^2}{({x'}^{2}+{y'}^{2}+{z'}^{2})^3}.$
differential-geometry
edited yesterday
mathcounterexamples.net
24.9k21853
asked yesterday
user505797
33
add a comment |
Find the curvature of the curve :
$ x = t - sin{t} $ , $y = 1 - cos{t} $ , $z=4sin{dfrac{t}{2}}$.
I have been trying to find the curvature using the formula
$ {k_{1}}^2 = dfrac{{begin{vmatrix} x''& y'' \ x' & y' end{vmatrix}}^2 +{begin{vmatrix} y'' & z'' \ y' & z' end{vmatrix}}^2 + {begin{vmatrix} z'' & x'' \ z' & x' end{vmatrix}}^2}{({x'}^{2}+{y'}^{2}+{z'}^{2})^3}.$
differential-geometry
edited yesterday
mathcounterexamples.net
24.9k21853
asked yesterday
user505797
33
What have you try? Thanks!
– mathcounterexamples.net
yesterday
I was using the direct formula for the curvature given in the book A. Pogorelov Geometry, but not able to find precise answer. Shall I attach the image of my work, Sir?
– user505797
yesterday
Try to apply the formula of the book and write done what you did!
– mathcounterexamples.net
yesterday
I have added the formula Sir. It seems the answer is straight. But I'm lost in calculation.
– user505797
yesterday
You have the formula already, so just plug in the expressions for $x, y, z$ and simplify (and just leave that as answer).
– Arctic Char
yesterday
add a comment |
Find the curvature of the curve :
$ x = t - sin{t} $ , $y = 1 - cos{t} $ , $z=4sin{dfrac{t}{2}}$.
I have been trying to find the curvature using the formula
$ {k_{1}}^2 = dfrac{{begin{vmatrix} x''& y'' \ x' & y' end{vmatrix}}^2 +{begin{vmatrix} y'' & z'' \ y' & z' end{vmatrix}}^2 + {begin{vmatrix} z'' & x'' \ z' & x' end{vmatrix}}^2}{({x'}^{2}+{y'}^{2}+{z'}^{2})^3}.$
differential-geometry
edited yesterday
mathcounterexamples.net
24.9k21853
asked yesterday
user505797
33
Find the curvature of the curve :
$ x = t - sin{t} $ , $y = 1 - cos{t} $ , $z=4sin{dfrac{t}{2}}$.
I have been trying to find the curvature using the formula
$ {k_{1}}^2 = dfrac{{begin{vmatrix} x''& y'' \ x' & y' end{vmatrix}}^2 +{begin{vmatrix} y'' & z'' \ y' & z' end{vmatrix}}^2 + {begin{vmatrix} z'' & x'' \ z' & x' end{vmatrix}}^2}{({x'}^{2}+{y'}^{2}+{z'}^{2})^3}.$
differential-geometry
differential-geometry
edited yesterday
mathcounterexamples.net
24.9k21853
asked yesterday
user505797
33
edited yesterday
mathcounterexamples.net
24.9k21853
asked yesterday
user505797
33
edited yesterday
mathcounterexamples.net
24.9k21853
edited yesterday
mathcounterexamples.net
24.9k21853
edited yesterday
mathcounterexamples.net
24.9k21853
24.9k21853
asked yesterday
user505797
33
asked yesterday
user505797
33
asked yesterday
user505797
33
33
What have you try? Thanks!
– mathcounterexamples.net
yesterday
I was using the direct formula for the curvature given in the book A. Pogorelov Geometry, but not able to find precise answer. Shall I attach the image of my work, Sir?
– user505797
yesterday
Try to apply the formula of the book and write done what you did!
– mathcounterexamples.net
yesterday
I have added the formula Sir. It seems the answer is straight. But I'm lost in calculation.
– user505797
yesterday
You have the formula already, so just plug in the expressions for $x, y, z$ and simplify (and just leave that as answer).
– Arctic Char
yesterday
add a comment |
What have you try? Thanks!
– mathcounterexamples.net
yesterday
I was using the direct formula for the curvature given in the book A. Pogorelov Geometry, but not able to find precise answer. Shall I attach the image of my work, Sir?
– user505797
yesterday
Try to apply the formula of the book and write done what you did!
– mathcounterexamples.net
yesterday
I have added the formula Sir. It seems the answer is straight. But I'm lost in calculation.
– user505797
yesterday
You have the formula already, so just plug in the expressions for $x, y, z$ and simplify (and just leave that as answer).
– Arctic Char
yesterday
What have you try? Thanks!
– mathcounterexamples.net
yesterday
What have you try? Thanks!
– mathcounterexamples.net
yesterday
I was using the direct formula for the curvature given in the book A. Pogorelov Geometry, but not able to find precise answer. Shall I attach the image of my work, Sir?
– user505797
yesterday
I was using the direct formula for the curvature given in the book A. Pogorelov Geometry, but not able to find precise answer. Shall I attach the image of my work, Sir?
– user505797
yesterday
Try to apply the formula of the book and write done what you did!
– mathcounterexamples.net
yesterday
Try to apply the formula of the book and write done what you did!
– mathcounterexamples.net
yesterday
I have added the formula Sir. It seems the answer is straight. But I'm lost in calculation.
– user505797
yesterday
I have added the formula Sir. It seems the answer is straight. But I'm lost in calculation.
– user505797
yesterday
You have the formula already, so just plug in the expressions for $x, y, z$ and simplify (and just leave that as answer).
– Arctic Char
yesterday
You have the formula already, so just plug in the expressions for $x, y, z$ and simplify (and just leave that as answer).
– Arctic Char
yesterday
add a comment |
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What have you try? Thanks!
– mathcounterexamples.net
yesterday
I was using the direct formula for the curvature given in the book A. Pogorelov Geometry, but not able to find precise answer. Shall I attach the image of my work, Sir?
– user505797
yesterday
Try to apply the formula of the book and write done what you did!
– mathcounterexamples.net
yesterday
I have added the formula Sir. It seems the answer is straight. But I'm lost in calculation.
– user505797
yesterday
You have the formula already, so just plug in the expressions for $x, y, z$ and simplify (and just leave that as answer).
– Arctic Char
yesterday