Hey
I am trying to calculate the streamline of u=(ay, -ax, 0)
I know i need to solve this set of differential equations:
dx/ds = ay, dy/ds= -ax , dz/ds=0
I am supposed to get a solution of:
x = yo sin (as) + xo cos (as)
y = yo cos (as) - xo sin (as)
z = zo
where xo, yo, zo are the intial conditions.
I don't understand where the sin and cos have come from.
Thank you for any help
By the way, to find just the streamlines (without knowing when you are at a particular point on the streamlines), you can eliminate the variable s. Since and , . That is a separable equation: so or . Fortunately, so z is a constant. The streamlines are circles, in the plane , with center at . You should be able to see that this is exactly what x = yo sin (as) + xo cos (as)
y = yo cos (as) - xo sin (as)
z = zo
considered as parametric equations in the parameter s, give.