COPYRIGHT NOTICE
Copyright 2007 Samuel Dagan
dagan@post.tau.ac.il
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Rotation of coordinates
Planar rotation as a transformation.
The origin of the figure is at (0,0)
©
Samuel Dagan
Rotation of coordinates
x
y
x'
y'
-3
-2
-1
1
2
3
-3
-2
-1
1
2
3
Δφ
Δφ
A rotation of coordinates
is illustrated using the level
lines z ≥ 0
of an ellipsoid .
The rotation of a function by
an angle Δφ
about the origin
is defined by the relations
x = x'cos(Δφ)+y'sin(Δφ)
and
y = −x'sin(Δφ)+y'cos(Δφ)
with (x',y' ) as new
variables.
The drawn Δφ = π⁄4 will
be
used for the next
animation.
The large diameter of the
ellipsoid's projection raised
from zero to a positive Δφ
toward the abscissa.
A rotation of the coordinates
from (x,y) to (x',y' ) by an
angle Δφ
about the origin
is defined by the relations
x = x'cos(Δφ)−y'sin(Δφ)
and
y = x'sin(Δφ)+y'cos(Δφ) ,
as shown after resetting.
The drawn Δφ =
−π⁄4 will
be
used for the next
animation.
The final relative position
of the ellipsoid toward the
coordinate system is the
same as before.
restart
Use the zoom of your system
to resize this window
Use the mouse to pan and
to resize the graphics
ani-
mate
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