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Topic: Vector Components after Coordinate Transformations
Replies: 0

 dreamer Posts: 1 Registered: 5/7/14
Vector Components after Coordinate Transformations
Posted: May 7, 2014 8:25 AM

I am facing difficulty in understanding the vector component in 2
different co ordinate systems. Kindly help me.

Suppose I have a vector A on the 2d co ordinate system x and y and
therefore vector A = A_x*i + A_y*j where i and j are unit vectors along
x and y axis.

Suppose a new co ordinate system is introduced in which is x',y' and is
titlted from the x,y plane by angle theta and both the co ordinate
systems (x,y and x',y') share the same origin.

The component of the vector seem to change on x',y' plane.

A = i'*A_x' + j'*A_y' (i' and j' are the unit vectors along the x' and
y')

and now i' = i cos (theta) + j sin (theta)
j' = - i sin (theta) + j cos (theta)

Kindly help me understand the concept.