Rolling an Ellipse along a curve
First, let us roll an ellipse along a horizontal line, y=d. If the equation of the ellipse, whose center is it (LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRImNGJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRictSSNtb0dGJDYtUSIsRicvRjZRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRkgvJSpzeW1tZXRyaWNHRkgvJShsYXJnZW9wR0ZILyUubW92YWJsZWxpbWl0c0dGSC8lJ2FjY2VudEdGSC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYsNiUtRi82JVEieUYnRjJGNUY4Rj1GRA== ), is expressed in parametric form, we have
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
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYsLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInRGJ0YvRjIvRjNRJ25vcm1hbEYnRj0tSSNtb0dGJDYtUSJ+RidGPS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZULUZANi1RIj1GJ0Y9RkNGRkZIRkpGTEZORlAvRlNRLDAuMjc3Nzc3OGVtRicvRlZGZW5GPy1JJW1zdWJHRiQ2JUYrLUYjNiUtRiw2JVEiY0YnRi9GMkYvRjIvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1GQDYtUSIrRidGPUZDRkZGSEZKRkxGTkZQL0ZTUSwwLjIyMjIyMjJlbUYnL0ZWRmZvLUYsNiVRJWJzaW5GJ0YvRjJGNUY9
The ellipse is drawn, starting at the point 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 , and revolves in a counter-clockwise fashion. Next, notice that in order for the ellipse to be resting, initially, on the line LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSJkRidGL0YyRjk= , we must have that 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 .
First we graph the line and ellipse.
restart:
with(plots): with(plottools): with(linalg):
xc:=2;yc:=4;
IiIj
IiIl
a:=4;b:=2;
IiIl
IiIj
EllipseF:=t->[xc+a*cos(t),yc+b*sin(t)];
Zio2I0kidEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlNyQsJkkjeGNHRiUiIiIqJkkiYUdGJUYsLUkkY29zR0YlNiM5JEYsRiwsJkkjeWNHRiVGLComSSJiR0YlRiwtSSRzaW5HRiVGMUYsRixGJUYlRiU=
plot1:=plot([xc+a*cos(t),yc+b*sin(t),t=0..2*Pi], scaling=constrained, color=red, thickness=3, labels=[x,y]):
plot2:=plot(2,x=-10..20,color=magenta,thickness=2):
display({plot1,plot2},view=[-10..20,0..30]);
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
plot3:=pointplot([xc,yc],symbol=cross,symbolsize=10, color=black):
display({plot1,plot2,plot3},view=[-10..20,0..30]);
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
So if we wish to roll the ellipse r units in the x-direction, then we must count out r units on the ellipse, in a counter-clockwise direction, starting at the point on the ellipse which is touching the line. To find the angle of rotation needed to roll the ellipse r units to the right, we need two vectors, both starting at the center of the ellipse, with the first being from the center to the current location of where the ellipse touches the line, the second to the future location where the ellipse will touch the line.
The formula for arcelength of a parametric curuve for 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 is given by
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
For our first roll, 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 , and we need to figure out at what time LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMUYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y+ , we have swept out r units in arclength.
First, we calculate the total arclenth of the ellipse, using 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 and 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 , which gives a full revolution.
evalf(int(sqrt(diff(a*cos(t),t)^2+diff(b*sin(t),t)^2),t=0..2*Pi));
JCIrVicqb1A+ISIp
We set LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjJGJ0Y5Rjk= , which is reasonably small in comparison to the arclength of the ellipse. We need to find the time corresponding to the point (x,y) which is the end of the arclength 2 arc starting at the point on the ellipse which touches the line. (We are assuming counter-clockwise direction since the ellipse is moving to the right). Setting arclength to 2, gives the equation
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
In order to get the correct solution value for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMUYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y+ , we need to make sure that 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 . We will use the fsolve command, with the extra option of limiting the range to search for solutions.
fsolve(2 = evalf(int(sqrt(16*sin(t)^2+4*cos(t)^2),t=3*Pi/2..t1)),t1,3*Pi/2..2*Pi);
Warning, unable to determine if Pi*_Z12 is between (3/2)*Pi and t1; try to use assumptions or use the AllSolutions option
JCIrI0dRI0hfISIq
We plot the difference of 2 and the arclength formula, notice the roots here correspond to t values which give arclength 2.
plot(2 - evalf(int(sqrt(16*sin(t)^2+4*cos(t)^2),t=3*Pi/2..t1)),t1=0..2*Pi);
LSUlUExPVEc2Ji0lJ0NVUlZFU0c2JDdTNyQkIiIhISIiJCIrTHNFYDshIik3JCQiKyZlYiZwOCEjNSQiKzFCaUQ7ISIpNyQkIit3Jik+aEQhIzUkIitCLFYrOyEiKTckJCIqdkQ4IVIhIiokIislRzUpcDohIik3JCQiK2RoTF1fISM1JCIrOkIjZWAiISIpNyQkIitgXCRIZichIzUkIit0PFopXCIhIik3JCQiKyxmcFB5ISM1JCIrTCNcMVkiISIpNyQkIitqUGRFIiohIzUkIitUK1M9OSEiKTckJCIrNEwmZi8iISIqJCIrZSx0cjghIik3JCQiKndAKXk2ISIpJCIrRlVtQTghIik3JCQiKyVIJFw6OCEiKiQiK28oUSxGIiEiKTckJCIrYk8oZVYiISIqJCIrejdwQTchIik3JCQiKlYkUnI6ISIpJCIrIilmZ282ISIpNyQkIitpJ3B1cSIhIiokIiokSEk5NiEiKDckJCIrRVZnUT0hIiokIitbZm5pNSEiKTckJCIranJvZD4hIiokIitaZSVwLCIhIik3JCQiK3YiKUcqNCMhIiokIiswXVhZJyohIio3JCQiKzFHQz5BISIqJCIrIj1nZUEqISIqNyQkIitmJnkoZUIhIiokIisnUidRbigpISIqNyQkIitWOEgjWyMhIiokIistOj8jUikhIio3JCQiK1ZXIXloIyEiKiQiK3ppUDohKSEiKjckJCIraFwlb3UjISIqJCIqRGwpKm8oISIpNyQkIisuX1siKUchIiokIiskNDo4USghIio3JCQiK3dwNzBJISIqJCIrLW5tPnIhIio3JCQiK0s4XFFKISIqJCIrJ3lFLyZvISIqNyQkIis7JT5xRiQhIiokIitOZSI0ZCchIio3JCQiKl8zd1IkISIpJCIrRSwzO2ohIio3JCQiK2MhW3lfJCEiKiQiKzBwIyo9ZyEiKjckJCIrVCMpUmlPISIqJCIrLmMmNG8mISIqNyQkIitaJEhTeiQhIiokIis4bkA7YCEiKjckJCIrNiMqUUBSISIqJCIrZDFlSVwhIio3JCQiK0QxIUcxJSEiKiQiK3UpemtZJSEiKjckJCIqMmwpKj0lISIpJCIrej5cP1MhIio3JCQiKyhbTGJLJSEiKiQiK1doJik9TiEiKjckJCIrTyNwJVtXISIqJCIrOVBhWUkhIio3JCQiKyNbcUdlJSEiKiQiK2AjKilwXiMhIio3JCQiKyJlSiQ0WiEiKiQiKydlSEEsIyEiKjckJCIrbik+OiVbISIqJCIrKlxeWFsiISIqNyQkIit5IWUyKFwhIiokIipKbjR2KiEiKjckJCIrMyZlZzUmISIqJCIpXjRhWCEiKTckJCIrLipvakImISIqJCEpR0N1RCEiKjckJCIrLixqcGAhIiokISotYV0jXCEiKjckJCIrTHl5LGIhIiokISo4RmBEKiEiKjckJCIraHFBQmMhIiokISsicElWSCIhIio3JCQiK0EsVGlkISIqJCErbmUuIm8iISIqNyQkIio2KCpvKWUhIikkISs6KnlbKj4hIio3JCQiKy9paT5nISIqJCErUnhjKkgjISIqNyQkIiskKVttWWghIiokIStFIXAnb0QhIio3JCQiKyZIJj0kRychIiokISskM0NVJUchIiotJSZDT0xPUkc2JiUkUkdCRyQiIzUhIiIkIiIhISIiJCIiISEiIi0lJVZJRVdHNiQ7JCIiISEiIiQiKzNgPSRHJyEiKiUoREVGQVVMVEctJStBWEVTTEFCRUxTRzYkLUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHNiI2NVEjdDE2Ii8lJ2ZhbWlseUdRITYiLyUlc2l6ZUdRIzEwNiIvJSVib2xkR1EmZmFsc2U2Ii8lJ2l0YWxpY0dRJXRydWU2Ii8lKnVuZGVybGluZUdRJmZhbHNlNiIvJSpzdWJzY3JpcHRHUSZmYWxzZTYiLyUsc3VwZXJzY3JpcHRHUSZmYWxzZTYiLyUrZm9yZWdyb3VuZEdRKFswLDAsMF02Ii8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdNiIvJSdvcGFxdWVHUSZmYWxzZTYiLyUrZXhlY3V0YWJsZUdRJmZhbHNlNiIvJSlyZWFkb25seUdRJmZhbHNlNiIvJSljb21wb3NlZEdRJmZhbHNlNiIvJSpjb252ZXJ0ZWRHUSZmYWxzZTYiLyUraW1zZWxlY3RlZEdRJmZhbHNlNiIvJSxwbGFjZWhvbGRlckdRJmZhbHNlNiIvJTZzZWxlY3Rpb24tcGxhY2Vob2xkZXJHUSZmYWxzZTYiLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWM2IlEhNiItJSVST09URzYnLSUpQk9VTkRTX1hHNiMkIiRJJSEiIi0lKUJPVU5EU19ZRzYjJCIjXSEiIi0lLUJPVU5EU19XSURUSEc2IyQiJT9OISIiLSUuQk9VTkRTX0hFSUdIVEc2IyQiJSEpUSEiIi0lKUNISUxEUkVORzYi
EllipseF(5.229238282);
NyQkIitlUGR3UiEiKiQiK0EjUjdFI0Yl
plot4:=pointplot([EllipseF(3*Pi/2),EllipseF(5.229238282)],symbol=diamond, symbolsize=20,color=GREEN):
plot5:=pointplot([4,2],symbol=circle, symbolsize=20, color=black):
display({plot1,plot2,plot3,plot4,plot5},view=[-3..10,-3..10]);
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
display({plot1,plot2,plot3,plot4,plot5},view=[1..5,1..3], scaling=constrained);
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bHNlNiIvJSljb21wb3NlZEdRJmZhbHNlNiIvJSpjb252ZXJ0ZWRHUSZmYWxzZTYiLyUraW1zZWxlY3RlZEdRJmZhbHNlNiIvJSxwbGFjZWhvbGRlckdRJmZhbHNlNiIvJTZzZWxlY3Rpb24tcGxhY2Vob2xkZXJHUSZmYWxzZTYiLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWM2IlEhNiItJSVGT05URzYlJShERUZBVUxURyUoREVGQVVMVEciIzUtJShTQ0FMSU5HRzYjJSxDT05TVFJBSU5FREctJSVST09URzYnLSUpQk9VTkRTX1hHNiMkIiRnJSEiIi0lKUJPVU5EU19ZRzYjJCIlPzghIiItJS1CT1VORFNfV0lEVEhHNiMkIiUhKVwhIiItJS5CT1VORFNfSEVJR0hURzYjJCIlIVwjISIiLSUpQ0hJTERSRU5HNiI=
Now we need to rotate the ellipse. But we are missing one important piece of information. What is it? We need the angle of rotation. Consider the two displacement vectors starting at the point on the ellipse touching the line, and ending at the next point on the line the ellipse will be located at, and the second point on the ellipse. The angle between them may give us the angle of rotation.
EllipseF(t);
NyQsJiIiIyIiIi1JJGNvc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSJ0R0YrIiIlLCZGLkYlLUkkc2luR0YoRixGJA==
M:=diff(EllipseF(t),t)[2]/diff(EllipseF(t),t)[1];
LCQqJi1JJGNvc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSJ0R0YpIiIiLUkkc2luR0YmRiohIiIjRi8iIiM=
m:=evalf(subs(t=5.229238282, M));
JCIrTylHPiVHISM1
solve(subs({y=2},y-EllipseF(5.229238282)[2] = m*(x-EllipseF(5.229238282)[1])),x);
JCIrYjtNZEkhIio=
plot6:=pointplot([3.057341655,2],symbol=circle, color=BLUE, symbolsize=20):
plot7:=plot(EllipseF(5.229238282)[2] + m*(x-EllipseF(5.229238282)[1]),x=3..4.2, thickness=2, color=BLACK):
display({plot1,plot2,plot3,plot4,plot5,plot6,plot7},view=[2..4.55,1.5..2.5], scaling=constrained);
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
Center:=[3.057341655,2];
NyQkIitiO01kSSEiKiIiIw==
Top:=EllipseF(5.229238282);
NyQkIitlUGR3UiEiKiQiK0EjUjdFI0Yl
Bottom:=[4,2];
NyQiIiUiIiM=
u:=<Top-Center>;
LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqI0hjKm8i
v:=<Bottom-Center>;
LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqa0heJD0=
theta_r:=VectorAngle(u,v);
JCIrXF4jKm9GISM1
evalf(%*180/Pi);
JCIrW3NaJ2UiISIp
So from above, we have approximately 15.86 degrees to rotate, or 0.27 radians. So now we need to move the ellipse to the origin, and then rotate, and finally place it back in its new correct location.
EllipseCol:=matrix(2,1,EllipseF(t)-[2,4]);
PTYiNiQ7IiIiIiIjO0YmRiZFXFtsIzYkRiZGJiwkLUkkY29zRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YjNiNJInRHRiMiIiU2JEYnRiYsJC1JJHNpbkdGLkYxRic=
Atheta:= theta -> matrix(2,2,[cos(theta), -sin(theta), sin(theta), cos(theta)]);
Zio2I0kmdGhldGFHNiJGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJS1fSSdsaW5hbGdHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiVJJ21hdHJpeEdGLDYlIiIjRjE3Ji1JJGNvc0dGLDYjOSQsJC1JJHNpbkdGLEY1ISIiRjhGM0YlRiVGJQ==
NewEllipse:=evalm(Atheta(-theta_r)&*EllipseCol);
PTYiNiQ7IiIiIiIjO0YmRiZFXFtsIzYkRiZGJiwmLUkkY29zRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YjNiNJInRHRiMkIityI1F3JVEhIiotSSRzaW5HRi5GMSQiK3NxTm5hISM1NiRGJ0YmLCZGLCQhKzk5WiQ0IkY1RjYkIitPIj5RIz5GNQ==
plot8:=plot([NewEllipse[1,1]+2,NewEllipse[2,1]+4, t=0..2*Pi], color=BLUE, thickness=2):
display({plot1,plot2,plot3,plot4,plot5,plot6, plot7,plot8},view=[-4..10,-4..10]);
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We have sucessfully rotated the ellipse, now we need to move it into the correct position!
print(NewEllipse);
SStOZXdFbGxpcHNlRzYi
plot9a:=plot([NewEllipse[1,1],NewEllipse[2,1], t=0..Pi], color=BLUE, thickness=2, scaling=constrained):
plot9b:=plot([NewEllipse[1,1],NewEllipse[2,1], t=Pi..2*Pi], color=GREEN, thickness=2, scaling=constrained):
display({plot8a,plot8b});
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
print(NewEllipse);
SStOZXdFbGxpcHNlRzYi
LowestPoint:=[evalf(subs({t=5.229238282}, NewEllipse[1,1])),evalf(subs({t=5.229238282}, NewEllipse[2,1]))];
NyQkIiszUidmVSIhIiokIStiQidHQCNGJQ==
plot10:=pointplot(LowestPoint,color=black, symbol=circle, symbolsize=20):
display({plot9a,plot9b, plot10});
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
display({plot9a,plot9b, plot10}, view=[1..2,-2.3..-2]);
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
NewEllipse[2,1];
LCYtSSRjb3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kidEdGKCQhKzk5WiQ0IiEiKi1JJHNpbkdGJUYpJCIrTyI+USM+Ri0=
minimize(NewEllipse[2,1],t=5..5.6);
JCErYkInR0AjISIq
LowestPoint;
NyQkIiszUidmVSIhIiokIStiQidHQCNGJQ==
ShifT:=Bottom-LowestPoint;
NyQkIisjNE9TZCMhIiokIitiQidHQCVGJQ==
NewNewEllipse:=evalm(NewEllipse+ShifT);
PTYiNiQ7IiIiIiIjO0YmRiZFXFtsIzYkRiZGJiwoLUkkY29zRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YjNiNJInRHRiMkIityI1F3JVEhIiotSSRzaW5HRi5GMSQiK3NxTm5hISM1JCIrIzRPU2QjRjVGJjYkRidGJiwoRiwkISs5OVokNCJGNUY2JCIrTyI+USM+RjUkIitiQidHQCVGNUYm
plot11:=plot([NewNewEllipse[1,1],NewNewEllipse[2,1], t=0..2*Pi], color=BLUE, thickness=2, scaling=constrained):
plot12:=pointplot(ShifT,color=black, symbol=cross, symbolsize=10):
display({plot1,plot2,plot3,plot4,plot5,plot11,plot12},view=[-3..10,-3..10]);
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
[2.574036092, 4.212862355];
NyQkIisjNE9TZCMhIiokIitiQidHQCVGJQ==
evalm(subs({t=Pi},NewNewEllipse[1,1]));
JCErekBndDchIio=
evalm(subs({t=0},NewNewEllipse[1,1]));
JCIralZuQGshIio=
(6.421674363+(-1.273602179))/2;
JCIrIzRPU2QjISIq
evalm(subs({t=Pi},NewNewEllipse[2,1]));
JCIrcFBMMWAhIio=
evalm(subs({t=0},NewNewEllipse[2,1]));
JCIrVDRSPkohIio=
(5.306333769+3.119390941)/2;
JCIrYkInR0AlISIq
evalf(11/8*Pi);
JCIrKiopKm8+ViEiKg==
19.37689643/4;
JCIrM1RBV1shIio=
TTdSMApJNlJUQUJMRV9TQVZFLzE2ODk1NjI5MlgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiMiIyQiKi5AQj4qISIqJCIqQSNSN0VGKUYm TTdSMApJNlJUQUJMRV9TQVZFLzE4MzUxMjk2NFgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiMiIyQiKlgkZUUlKiEiKiIiIUYm