Understanding the Flow of a Vector Field: Basics and Calculations

[ductape]

Hello, I am having a lot of trouble finding a definition of a flow generated by a vector field. I can't seem to find a good definition anywhere. I only need a basic definition, and a basic approach to calculating the flow generated by a vector field.
For example, Let U = R2 , x = x(u, v, 0). Let M = x(U). Let V be a vector field who's coordinate expression is as follows: V(hat) = (v,u). What is the flow generated by V. I am only looking at curves and surfaces in R3. Any help would be greatly appreciated.

 

[tiny-tim]

For example, Let U = R2 , x = x(u, v, 0). Let M = x(U). Let V be a vector field who's coordinate expression is as follows: V(hat) = (v,u). What is the flow generated by V. I am only looking at curves and surfaces in R3. Any help would be greatly appreciated.

Hello ductape!

I don't think there's such a thing as a flow generated by a vector field …

the vector field is the flow …

for example, the vector field (u,v) would be radial.

I don't understand V(hat) = (v,u) either. V(hat) usually means a unit vector, and (v,u) isn't a unit vector.

If it was V = (v,u), then that would be the flow whose vector is (v,u) at every point (u,v).

 

[mathwonk]

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