Understanding Rotating Coordinate Systems: A Visual Approach

AI Thread Summary
The discussion focuses on understanding the equations related to rotating coordinate systems, specifically the transformations involving variables x, y, u, and v. The user struggles to visualize the relationship between these variables, particularly how u can be expressed in terms of x and y. A suggestion is made to manipulate the equations by multiplying them with trigonometric functions, which leads to a clearer understanding. Despite following this advice, the user still finds it challenging to grasp the visual aspect of the transformation. The conversation highlights the need for visual aids or further clarification to aid comprehension of rotating coordinate systems.
xzibition8612
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Homework Statement



http://www.brookscole.com/math_d/sp...athematica_labs/14-multipleintegrals/p05a.pdf



Homework Equations





The Attempt at a Solution



My question concerns the (1) and (2) next to the figure of the rotating coordinate system.

x=ucos(theta)-vsin(theta)
y=ucos(theta)...
...

So my problem is I can't visualize it. I can visualize that u = ucos(theta) + usin(theta), but I don't get how u = xcos(theta) + ysin(theta).
If anyone can explain or try to visually show it to me would be great. Thanks.
 
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Hi,xzibition8612.

Multiply both side of equatlity (1) x=ucos(theta)-vsin(theta) with cos(theta) and both of equality y=ucos(theta)...with sin(theta) you will see some terms will vanish.And you will get your answer...
 
ok i did as you said and got u = sin(theta)y + xcos(theta) which is (2). I still don't get how come u is this quantity. I mean in a visual manner. I'm not so smart to understand it abstractly. Sorry for my poor intelligence.
 
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