Sine Curve Circular Transform - Parametric Equations
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Is there a way to transform a sine curve so that the x-axis of the sine curve would become a circle, with the sine wave oscillating around the now-circular x-axis?
What would be the parametric equations of such a curve? Any ideas?
transformation curves parametrization
edited Nov 22 at 23:49
Eric Wofsey
177k12202328
asked May 16 '16 at 0:08
skrug4670
1
add a comment |
up vote
0
down vote
favorite
Is there a way to transform a sine curve so that the x-axis of the sine curve would become a circle, with the sine wave oscillating around the now-circular x-axis?
What would be the parametric equations of such a curve? Any ideas?
transformation curves parametrization
edited Nov 22 at 23:49
Eric Wofsey
177k12202328
asked May 16 '16 at 0:08
skrug4670
1
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Is there a way to transform a sine curve so that the x-axis of the sine curve would become a circle, with the sine wave oscillating around the now-circular x-axis?
What would be the parametric equations of such a curve? Any ideas?
transformation curves parametrization
edited Nov 22 at 23:49
Eric Wofsey
177k12202328
asked May 16 '16 at 0:08
skrug4670
1
Is there a way to transform a sine curve so that the x-axis of the sine curve would become a circle, with the sine wave oscillating around the now-circular x-axis?
What would be the parametric equations of such a curve? Any ideas?
transformation curves parametrization
transformation curves parametrization
edited Nov 22 at 23:49
Eric Wofsey
177k12202328
asked May 16 '16 at 0:08
skrug4670
1
edited Nov 22 at 23:49
Eric Wofsey
177k12202328
asked May 16 '16 at 0:08
skrug4670
1
edited Nov 22 at 23:49
Eric Wofsey
177k12202328
edited Nov 22 at 23:49
Eric Wofsey
177k12202328
edited Nov 22 at 23:49
Eric Wofsey
177k12202328
177k12202328
asked May 16 '16 at 0:08
skrug4670
1
asked May 16 '16 at 0:08
skrug4670
1
asked May 16 '16 at 0:08
skrug4670
1
1
add a comment |
add a comment |
1 Answer
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Such a curve would have a polar representation
$$r(phi)=a+bsin(n,phi)qquad(-infty<phi<infty) ,tag{1}$$
whereby $agg b>0$, and $n>0$ (not necessarily an integer) denotes the number of full periods per one turn around the origin. The representation $(1)$ can be rewritten as a parametric representation as follows:
$$x(phi)=bigl(a+bsin(n,phi)bigr)cosphi,quad y(phi)=bigl(a+bsin(n,phi)bigr)sinphi .$$
answered May 16 '16 at 8:07
Christian Blatter
171k7111325
Do you know how this is derived or what it signifies? For example, I know that the hypocycloid and epicycloid curves are the paths created by a point P on a circumference of a smaller circle that is rolling on the inside and outside of a bigger circle, respectively, but is there such a model created for these parametric equations?
– skrug4670
May 20 '16 at 21:32
Also, would you happen to know how to increase the amplitude of the sine wave, while at the same time keeping the same angular proportions?
– skrug4670
May 22 '16 at 3:17
add a comment |
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1 Answer
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up vote
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down vote
Such a curve would have a polar representation
$$r(phi)=a+bsin(n,phi)qquad(-infty<phi<infty) ,tag{1}$$
whereby $agg b>0$, and $n>0$ (not necessarily an integer) denotes the number of full periods per one turn around the origin. The representation $(1)$ can be rewritten as a parametric representation as follows:
$$x(phi)=bigl(a+bsin(n,phi)bigr)cosphi,quad y(phi)=bigl(a+bsin(n,phi)bigr)sinphi .$$
answered May 16 '16 at 8:07
Christian Blatter
171k7111325
Do you know how this is derived or what it signifies? For example, I know that the hypocycloid and epicycloid curves are the paths created by a point P on a circumference of a smaller circle that is rolling on the inside and outside of a bigger circle, respectively, but is there such a model created for these parametric equations?
– skrug4670
May 20 '16 at 21:32
Also, would you happen to know how to increase the amplitude of the sine wave, while at the same time keeping the same angular proportions?
– skrug4670
May 22 '16 at 3:17
add a comment |
up vote
0
down vote
Such a curve would have a polar representation
$$r(phi)=a+bsin(n,phi)qquad(-infty<phi<infty) ,tag{1}$$
whereby $agg b>0$, and $n>0$ (not necessarily an integer) denotes the number of full periods per one turn around the origin. The representation $(1)$ can be rewritten as a parametric representation as follows:
$$x(phi)=bigl(a+bsin(n,phi)bigr)cosphi,quad y(phi)=bigl(a+bsin(n,phi)bigr)sinphi .$$
answered May 16 '16 at 8:07
Christian Blatter
171k7111325
Do you know how this is derived or what it signifies? For example, I know that the hypocycloid and epicycloid curves are the paths created by a point P on a circumference of a smaller circle that is rolling on the inside and outside of a bigger circle, respectively, but is there such a model created for these parametric equations?
– skrug4670
May 20 '16 at 21:32
Also, would you happen to know how to increase the amplitude of the sine wave, while at the same time keeping the same angular proportions?
– skrug4670
May 22 '16 at 3:17
add a comment |
up vote
0
down vote
up vote
0
down vote
Such a curve would have a polar representation
$$r(phi)=a+bsin(n,phi)qquad(-infty<phi<infty) ,tag{1}$$
whereby $agg b>0$, and $n>0$ (not necessarily an integer) denotes the number of full periods per one turn around the origin. The representation $(1)$ can be rewritten as a parametric representation as follows:
$$x(phi)=bigl(a+bsin(n,phi)bigr)cosphi,quad y(phi)=bigl(a+bsin(n,phi)bigr)sinphi .$$
answered May 16 '16 at 8:07
Christian Blatter
171k7111325
Such a curve would have a polar representation
$$r(phi)=a+bsin(n,phi)qquad(-infty<phi<infty) ,tag{1}$$
whereby $agg b>0$, and $n>0$ (not necessarily an integer) denotes the number of full periods per one turn around the origin. The representation $(1)$ can be rewritten as a parametric representation as follows:
$$x(phi)=bigl(a+bsin(n,phi)bigr)cosphi,quad y(phi)=bigl(a+bsin(n,phi)bigr)sinphi .$$
answered May 16 '16 at 8:07
Christian Blatter
171k7111325
answered May 16 '16 at 8:07
Christian Blatter
171k7111325
answered May 16 '16 at 8:07
Christian Blatter
171k7111325
answered May 16 '16 at 8:07
Christian Blatter
171k7111325
171k7111325
Do you know how this is derived or what it signifies? For example, I know that the hypocycloid and epicycloid curves are the paths created by a point P on a circumference of a smaller circle that is rolling on the inside and outside of a bigger circle, respectively, but is there such a model created for these parametric equations?
– skrug4670
May 20 '16 at 21:32
Also, would you happen to know how to increase the amplitude of the sine wave, while at the same time keeping the same angular proportions?
– skrug4670
May 22 '16 at 3:17
add a comment |
Do you know how this is derived or what it signifies? For example, I know that the hypocycloid and epicycloid curves are the paths created by a point P on a circumference of a smaller circle that is rolling on the inside and outside of a bigger circle, respectively, but is there such a model created for these parametric equations?
– skrug4670
May 20 '16 at 21:32
Also, would you happen to know how to increase the amplitude of the sine wave, while at the same time keeping the same angular proportions?
– skrug4670
May 22 '16 at 3:17
Do you know how this is derived or what it signifies? For example, I know that the hypocycloid and epicycloid curves are the paths created by a point P on a circumference of a smaller circle that is rolling on the inside and outside of a bigger circle, respectively, but is there such a model created for these parametric equations?
– skrug4670
May 20 '16 at 21:32
Do you know how this is derived or what it signifies? For example, I know that the hypocycloid and epicycloid curves are the paths created by a point P on a circumference of a smaller circle that is rolling on the inside and outside of a bigger circle, respectively, but is there such a model created for these parametric equations?
– skrug4670
May 20 '16 at 21:32
Also, would you happen to know how to increase the amplitude of the sine wave, while at the same time keeping the same angular proportions?
– skrug4670
May 22 '16 at 3:17
Also, would you happen to know how to increase the amplitude of the sine wave, while at the same time keeping the same angular proportions?
– skrug4670
May 22 '16 at 3:17
add a comment |
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