How do you create equations with rotated axes?

Question

How do you create equations with rotated axes.
What are the kinds of equations with rotated axes.
Please give me examples.


^_^

Answer 1

If you're asking for the equation of, for example, a parabola tilted T radians...

y = x^2
x' = xcos(T) - ysin(T) = xcos(T) - (x^2)sin(T)
y' = xsin(T) + ycos(T) = xsin(T) + (x^2)cos(T)

Solve it from there and express it as a parametric; good luck.

Answer 2

Sine wave is one example. 60 hertz (cycles) is a full circle, any positional degree of a motor shaft can be calculated using the sine wave, although you can do it with polar coordinates (90 degrees, etc.).
An interesting example would be on a four jaw chuck in an engine lathe, there are usually 2 axis' to deal with (sometimes 3), but you use a dial indicator to adjust them before cutting the object, not equations.