Angle of elliptical sector The Next CEO of Stack OverflowNormal to Ellipse and Angle at Major AxisFinding the angle of a sectorFinding the eccentricity/focus/directrix of ellipses and hyperbolas under some rotationGiven area of sector and a starting angle from focus of an ellipse, finding angle needed to get area.Angle arising from circle rolling along an ellipseStart and end point of a rotated ellipseCreate Ellipse From Eccentricity And Semi-Minor AxisFind the Area of an Ellipse Given Shortest Distance and Longest Distance from a certain Focus to Circumference?Finding points on ellipse given point on another ellipse in 3 dimensionsHow to calculate the distance travelled by a car in an elliptical track after a certain time given its angular speed
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Angle of elliptical sector
The Next CEO of Stack OverflowNormal to Ellipse and Angle at Major AxisFinding the angle of a sectorFinding the eccentricity/focus/directrix of ellipses and hyperbolas under some rotationGiven area of sector and a starting angle from focus of an ellipse, finding angle needed to get area.Angle arising from circle rolling along an ellipseStart and end point of a rotated ellipseCreate Ellipse From Eccentricity And Semi-Minor AxisFind the Area of an Ellipse Given Shortest Distance and Longest Distance from a certain Focus to Circumference?Finding points on ellipse given point on another ellipse in 3 dimensionsHow to calculate the distance travelled by a car in an elliptical track after a certain time given its angular speed
$begingroup$
Is there any way to calculate angle of elliptical sector? I created the following diagram of an ellipse. I know all of the following information (in blue in the diagram):
$c$ (circuit),
$e$ (eccentricity),
$a$ (semi-major axis),
$b$ (semi-minor axis),
$alpha$ (angle between start of arc and semi-major axis),
$s_1$ (distance of one edge of arc from center)
$s_2$ (size of arc),
$S$ (area of sector)
I would like to calculate $varphi$ (angle of sector) from this information. Is this possible?
geometry conic-sections
asked Mar 18 at 21:15
MichalMichal
6
$endgroup$
add a comment |
$begingroup$
Is there any way to calculate angle of elliptical sector? I created the following diagram of an ellipse. I know all of the following information (in blue in the diagram):
$c$ (circuit),
$e$ (eccentricity),
$a$ (semi-major axis),
$b$ (semi-minor axis),
$alpha$ (angle between start of arc and semi-major axis),
$s_1$ (distance of one edge of arc from center)
$s_2$ (size of arc),
$S$ (area of sector)
I would like to calculate $varphi$ (angle of sector) from this information. Is this possible?
geometry conic-sections
asked Mar 18 at 21:15
MichalMichal
6
$endgroup$
$begingroup$
You will need to invert the incomplete elliptic integral of the second kind.
$endgroup$
– user
Mar 18 at 23:04
add a comment |
$begingroup$
Is there any way to calculate angle of elliptical sector? I created the following diagram of an ellipse. I know all of the following information (in blue in the diagram):
$c$ (circuit),
$e$ (eccentricity),
$a$ (semi-major axis),
$b$ (semi-minor axis),
$alpha$ (angle between start of arc and semi-major axis),
$s_1$ (distance of one edge of arc from center)
$s_2$ (size of arc),
$S$ (area of sector)
I would like to calculate $varphi$ (angle of sector) from this information. Is this possible?
geometry conic-sections
asked Mar 18 at 21:15
MichalMichal
6
$endgroup$
Is there any way to calculate angle of elliptical sector? I created the following diagram of an ellipse. I know all of the following information (in blue in the diagram):
$c$ (circuit),
$e$ (eccentricity),
$a$ (semi-major axis),
$b$ (semi-minor axis),
$alpha$ (angle between start of arc and semi-major axis),
$s_1$ (distance of one edge of arc from center)
$s_2$ (size of arc),
$S$ (area of sector)
I would like to calculate $varphi$ (angle of sector) from this information. Is this possible?
geometry conic-sections
geometry conic-sections
asked Mar 18 at 21:15
MichalMichal
6
asked Mar 18 at 21:15
MichalMichal
6
edited Mar 18 at 22:44
Michal
asked Mar 18 at 21:15
MichalMichal
6
asked Mar 18 at 21:15
MichalMichal
6
asked Mar 18 at 21:15
MichalMichal
6
6
$begingroup$
You will need to invert the incomplete elliptic integral of the second kind.
$endgroup$
– user
Mar 18 at 23:04
add a comment |
$begingroup$
You will need to invert the incomplete elliptic integral of the second kind.
$endgroup$
– user
Mar 18 at 23:04
$begingroup$
You will need to invert the incomplete elliptic integral of the second kind.
$endgroup$
– user
Mar 18 at 23:04
$begingroup$
You will need to invert the incomplete elliptic integral of the second kind.
$endgroup$
– user
Mar 18 at 23:04
add a comment |
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$begingroup$
You will need to invert the incomplete elliptic integral of the second kind.
$endgroup$
– user
Mar 18 at 23:04