(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The Hyperbolic coordinate system is given by: u=2xy and v=x^2 - y^2

a.) Find the unit vectors u and v in terms of u,v,x(hat),y(hat)

b.)Find the time derivatives of u(hat) and v(hat), your answers will have du/dt and dv/dt in them

2. Relevant equations

None really

3. The attempt at a solution

I found the unit vectors by

u(hat) = (du/dx)i + (du/dy)j

v(hat) = (dv/dx)i + (dv/dy)j

then I substituted in for x and y to give equations in terms of v and u

u(hat) = (sqrt(2))sqrt(sqrt(u^2 + v^2) - v))x(hat) + (sqrt(2))sqrt(sqrt(u^2 + v^2) +v))y(hat)

v(hat) = (sqrt(2))sqrt(sqrt(u^2 + v^2) + v))x(hat) + (-sqrt(2))sqrt(sqrt(u^2 + v^2) - v))y(hat)

I just don't understand how to take the time derivatives of these unit vectors, any help would be greatly appreciated.

Thanks

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# Time Derivatives of Unit Vectors

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