thanks, this worked for me. As for the

eqn1 := u = V * cos(a) * cos(b);

eqn2 := v = V*sin(b);

eqn3 := w = V*sin(a)*cos(b);

res:=solve({eqn1, eqn2, eqn3}, {V,a,b});

map(sin, res[3]);

simplify(%);

gives sin(b) = v / ( RootOf( _Z^2 - v^2 - w^2 - u^2);

map(x->x^2, %);

simplify(%);

gives

sin(b)^2 = v^2 / (v^2 + w^2 + u^2), which has no _Z , but is not right. is there a better way to eliminate _Z ?

I am trying to go from body-referenced aircraft velocities u, v, w, to angle of attack a, sideslip b, and total speed V. This is a standard problem for beginning aeronautics, I'm just wondering the best was to solve it with maple. Spefically, I would like to use the following relations to get short expressions for the derivatives of u, v, and w.

Given that

u = V * cos(a) * cos(b)

v = V*sin(b)

w = V*sin(a)*cos(b)

and all variables above...