> | restart; |
> | alias(u=u(theta,r),v=v(theta,r),fr=fr(theta,r),ftheta=ftheta(theta,r),PHI=PHI(theta,r),h=h(hteta)); |
> | alias(utheta=utheta(theta,r),ur=ur(theta,r),vtheta=vtheta(theta,r),vr=vr(theta,r)); |
> | EQN:=w*(vr+1/r^2*utheta+2/r*v+1/r^2*cos(theta)/sin(theta)*u+v*fr+1/r^2*u*ftheta)-(-1/r^3*v*u^2+v^2*vr+1/r^2*ur*u*v+1/r^2*u*v*vtheta+1/r^4*u^2*utheta)=0; |
> | EQN:=subs(w=v^2+1/r^2*u^2,EQN); |
> | u:=diff(PHI,theta):v:=diff(PHI,r):utheta:=diff(u,theta):ur:=diff(u,r):vtheta:=diff(v,theta):vr:=diff(v,r): |
> | PHI:=r-h(theta); |
> | EQN; |
> | simplify(%): |
> | %*r^4*sin(theta); |
> | simplify(%); |
> | subs(diff(h(theta),theta)=p(theta),%); |
> | EQN2:=diff(p(theta),theta)=solve(%,diff(p(theta),theta)); |
> |