Ellipse,polar equation 3D

  • Thread starter petra
  • Start date
9
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Main Question or Discussion Point

halo

I will start with ,ellipse in polar coordinates.
bold mean=vectors
polar equation:ellipse in 3d

major axis = a rem:a>b
minor axis = b
angle = theta
info angle between two lines
1e line : focus and point on the ellipse
2e line : focus and perihelion
u,v are unit vector
u is direction major axis
v is direction minor axis
c is vector (orgin to the center of the ellipse)
rem: center different from focus for ellipse
rem: center=focus only for circle
x is vector (orgin to point on the ellipse)

x=c+a*cos(theta)u+b*sin(theta)v (1)



? how can you find the relation between euler angles and (1).

? how unit u,v vector related to euler angles.

? how (1) is related to real observation on the sky.
 

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