Calculating the h factors Arfken 2.1.3

[russjack]

Homework Statement

The u v z coordinate system used frequently in electrostatics and hydrodynamics is defined by the u v z coordinate system which is xy=u x^2-y^2=v and z=z.
Sketch the system in the xy plane showing the surfaces of constant u and v.
Indicate the directions of the unit vectors. Is this coordinate system left handed or right handed.
And lastly calculate the h factors

Homework Equations

xy=u x^2-y^2=v and z=z.

The Attempt at a Solution

I found that the system was basically intersections of hyperbolas and the rational function 1/x. I found the system to left handed (I'm not quite sure if this is right). But I have no clue on where to even approach finding the h factors. Any suggestions?

 

[lanedance]

how much maths do you know? most of the examples quickly slip into some tensor notation, but there's a few that don't

the maths book by Riley Hobson Bence has a really good explanation in an appendix if I remember right

the scale factors help you calculate derivatives and integrals in different coordinate system, eg. they can be used to calculate that spherical coords need r.sin(theta) term in a volume integral, and similarly the representation of the grad, div & curl operators in a non-cartesian coord systems

 

[lanedance]

this is an example, though not the best
http://en.wikipedia.org/wiki/Curvilinear_coordinates#Orthogonal_curvilinear_coordinates

 

[lanedance]

actually section 10.10 in riley hobson bence

 

[lanedance]

actually looks like you need to read section 2 in Arfken