vector analysis, conversion between coordinate systems

[Karl Karlsson]

Hi! I am currently studying vectoranalysis at the university and I am not completely sure what the formulas [MATH]v_j = v^a\frac {\partial x^j} {\partial \chi^a}[/MATH] and [MATH]v^b = v^a\frac {\partial \chi^b} {\partial x^j}[/MATH] are saying. Is [MATH]v_j[/MATH] the j:th cartesian component of the vector [MATH]\vec v[/MATH] or could it hold for other bases as well? What does the second equation [MATH]v^b = v^a\frac {\partial \chi^b} {\partial x^j}[/MATH] mean? Is this just the relation between the b:th and a:th component of [MATH]\vec v[/MATH] being expressed as tangent vectors?

 

[yoscar04]

What book are you using? It looks like covariant formulation.
Where did you get the formulas?
You should define your variables, so people can help you where you got stuck.

 

[Dr.Peterson]

Can you show how this is defined in your book? Without context, we can't be sure what any of it means; and the notation seems very odd to me. Surely they tell you something about what the variables are?