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Forum Studenti •Formula di Stokes - Pagina 2
Pagina 2 di 2

Re: Formula di Stokes

Inviato: lunedì 30 giugno 2014, 17:03
da GIMUSI

Re: Formula di Stokes

Inviato: lunedì 30 giugno 2014, 19:28
da Gabe
Per questo esercizio la parametrizzazione del bordo mi torna cosi:

[tex]\delta\Omega_1=(1-t^2, t, 0), t \in [-1, 1][/tex]

[tex]\delta\Omega_2=(0, t, 0), t \in [-1, 1][/tex]

quindi il calcolo del flusso del [tex]rot(\overline{F})[/tex] su [tex]S[/tex], per questo verso della normale, applicando la formula di Stokes mi viene:

[tex]\int_{\delta\Omega_1} 0+(1-t^2)+0 dt - \int_{\delta\Omega_2} 0+0+0 dt = \int_{-1}^{1} (1-t^2) dt=4/3[/tex]

Re: Formula di Stokes

Inviato: lunedì 30 giugno 2014, 19:46
da Filippo.ingrasciotta
Si si, guardando il disegno di S ho visto dove sbagliavo ora mi tornano

Re: Formula di Stokes

Inviato: giovedì 3 luglio 2014, 21:44
da e.rapuano
Io non mi trovo con il risultato di questo esercizio:
la superficie è: x^2+y^2+z^2=4 con 0<=z<=1.
Il campo è F=(x, y+z, e^z)
Quando faccio il suo rotore mi esce rotF= (-1,0,0), il che è molto bello e mi ha indotto a pensare che sia meglio fare l'integrale di superficie del prodotto tra rotF e il versore normale alla superficie, piuttosto che parametrizzare il bordo...
Per parametrizzare la superficie...è giusto fare così? (u,v,sqrt(4 - u^2 - v^2))
Non è bellissimo da vedere...ma l'integrale non dovrebbe uscire troppo difficile...
a me esce zero...che non è il risultato giusto....quindi credo di aver sbagliato a integrare...
il dominio su cui integro è 0<= sqrt(4-u^2-v^2) <= 1 ??
è lecito svolgere le disequazioni fino ad arrivare a: 3<= u^2 + v^2 <= 4 ???
perchè io ho fatto così e poi ho proceduto con le coordinate polari....

Re: Formula di Stokes

Inviato: giovedì 3 luglio 2014, 21:57
da ghisi

Re: Formula di Stokes

Inviato: giovedì 3 luglio 2014, 22:20
da e.rapuano
:oops:
In qualche modo sono compiaciuto! XD
ahahahah
Si, non credo di aver sbagliato col versore... l'unica cosa è che ora mi viene il dubbio su molti esercizi che magari ho fatto bene e trovo il risultato sbagliato sul libro...
Riuscite a postare in qualche modo le soluzioni giuste degli esericizi riguardanti almeno gauss green e stokes? :D

Re: Formula di Stokes

Inviato: lunedì 14 luglio 2014, 18:19
da nomeutente
Ho un problema: sfera di raggio 1 con y, z>=0 normale esterna e devo calcolare il flusso di rotF con F=xz,y^2,ysinz
Che faccio?
Devo usare Stokes!!

Re: Formula di Stokes

Inviato: lunedì 14 luglio 2014, 23:13
da GIMUSI

Re: Formula di Stokes

Inviato: martedì 15 luglio 2014, 9:45
da nomeutente
Anche a me viene 0!!! La soluzione è 2/3..sarà sbagliata :)
Grazie GIMUSI :D