The idea is to write x,y,x as a function of s, i.e., x(s),y(s),z(s). If I can calculate r(s), then I can write x(r(s)),y(r(s)),z(r(s)), but I can't calculate r(s) from that equation
Hello, thank you for the answer. I have tried with the parametrization x=rcos(a), y=rsin(a), z=r^2, reaching to a similar expression: ds^2=1+4*r^2 (similar to yours with X=cos(a), Y=sin(a)). The solution is s = (1/4)*ln(2*r+sqrt(1+4*r^2))+(1/2)*r*sqrt(1+4*r^2), which is an equation in which I...
Hello,
I need the natural parametrization or a geodesic curve contained in the surface z=x^2+y^2, that goes through the origin, with x(s=0)=0, y(s=0)=0, dx/ds (s=0)=cos(a) and dy/ds(s=0)=sin(a), with "a" constant, expressed as a function of the arc length, i.e., I need r(s)=r(x(s),y(s)).
Thank...