lagranià de cordes

corda tub:

L(x,u,v) = a·x(u,v)+(-1)·h·( e^{iu}+e^{iv} )

constructor

d_{u}[L(x,u,v)] = a·d_{u}[x(u,v)]+(-1)·ih·e^{iu}

d_{v}[L(x,u,v)] = a·d_{v}[x(u,v)]+(-1)·ih·e^{iv}

x(u,v) = (h/a)·e^{iu}+(h/a)·e^{iv}

destructor:

d_{u}[x(u,v)] = (a/(hi))·e^{(-i)u}

d_{v}[x(u,v)] = (a/(hi))·e^{(-i)v}

x(u,v) = (a/h)·e^{(-i)u}+(a/h)·e^{(-i)v}

corda arc:

L(x,y,u,v) = (1/2)·a·( ( x(u) )^{2}+( y(v) )^{2} )+(e^{iu}+(-1)·e^{iv})·( e^{iu}+e^{iv} )

constructor

d_{u}[L(x,y,u,v)] = (1/2)·a·d_{u}[( x(u) )^{2}]+i·e^{2iu}

d_{v}[L(x,y,u,v)] = (1/2)·a·d_{v}[( y(v) )^{2}]+(-i)·e^{2iv}

x(u) = (1/a)^{(1/2)}·(j/i)·e^{iu}

y(v) = (1/a)^{(1/2)}·(k/i)·e^{iv}