Rotation of Rectangular Co-ordinates
(
X-Y plane
about
Z-axis
)
X - Y Rectangular Co-Ordinates
x=
y=
Angle of Rotation (
z
in degree) =
Find in
X1 - Y1 Rectangular Co-Ordinates
Angle of Rotation (angle Z in
Radian
)
Rotation Matrix K =
(k11)
(k12)
k11=cosz; k12=sinz;k21=-sinz;k22=cosz
(k21)
(k22)
Determinant & Trace
x1 (xcosz+ysinz) =
y1 (-xsinz+ycosz) =
Length in X-Y
Length in X1-Y1
Polar Co-ordinate
r=
√( x
2
+ y
2
)
Polar Co-ordinate
φ
(in radian)
= tan
-1
(y/x)
Polar Co-ordinate
φ
(in degree)
Rotation Matrix Kp (polar to polar co-ordinates) =
(kp11)
(kp12)
(kp11=1; kp12=0; kp21=0 ; kp22=1- (z/
φ)
(kp21)
(kp22)
Determinant & Trace
r1(r1=r)
φ1
in radian(φ1=z-φ)
φ1
in degree
Transformation Matrix
kpk
from Polar Co-ordinate (r1,
φ1
) to Rectangular Co-ordinate (x1.y1)
(kpr11)
(kpr12)
kpr11=cos
φ1 ; kpr12=0;kpr21=sinφ1; kpr22=0
(kpr21)
(kpr22)
Determinant & Trace
x1=
y1=
Transformation Matrix
kpp
from Rectangular Co-ordinate ( x,y) to Polar Co-ordinate (r,
φ
)
(kpp11)
(kpp12)
kpp11=
√( x
2
+ y
2
) / x ; kpp12=0 ;kpp21=0; kpp22=(1/y)*tan
-1
(y/x)
(kpp21)
(kpp22)
Determinant & Trace
r =
φ =
Overall transformation Matrix:(x,y) to (x1,y1)
(ot11)
(ot12)
ot11=cos(z-φ)*√( x
2
+ y
2
) / x = kpr11*kpp11 ; ot12=0; ot21=
sin(z
-φ)*√( x
2
+ y
2
) / x =kpr21*kpp11; ot22=0;
ot=kpk*kp*kpp
(ot21)
(ot22)
Determinant & Trace
x1=
y1=
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