Solução

Coordenadas Esféricas

[Graphics:../Images/Pratica3_gr_134.gif]
[Graphics:../Images/Pratica3_gr_135.gif]

O seguinte cálculo mostra que estes vectores são mútuamente ortogonais, e as suas normas são [Graphics:../Images/Pratica3_gr_136.gif], [Graphics:../Images/Pratica3_gr_137.gif] e [Graphics:../Images/Pratica3_gr_138.gif]

[Graphics:../Images/Pratica3_gr_139.gif]
[Graphics:../Images/Pratica3_gr_140.gif]
[Graphics:../Images/Pratica3_gr_141.gif]
[Graphics:../Images/Pratica3_gr_142.gif]
[Graphics:../Images/Pratica3_gr_143.gif]

[Graphics:../Images/Pratica3_gr_144.gif]

Coordenadas Parabólicas

[Graphics:../Images/Pratica3_gr_145.gif]
[Graphics:../Images/Pratica3_gr_146.gif]

O seguinte cálculo mostra que estes vectores são mútuamente ortogonais, e as suas normas são [Graphics:../Images/Pratica3_gr_147.gif], [Graphics:../Images/Pratica3_gr_148.gif] e [Graphics:../Images/Pratica3_gr_149.gif]

[Graphics:../Images/Pratica3_gr_150.gif]
[Graphics:../Images/Pratica3_gr_151.gif]
[Graphics:../Images/Pratica3_gr_152.gif]
[Graphics:../Images/Pratica3_gr_153.gif]
[Graphics:../Images/Pratica3_gr_154.gif]
[Graphics:../Images/Pratica3_gr_155.gif]
[Graphics:../Images/Pratica3_gr_156.gif]
[Graphics:../Images/Pratica3_gr_157.gif]
[Graphics:../Images/Pratica3_gr_158.gif]

[Graphics:../Images/Pratica3_gr_159.gif]

Gradiente em Coordenadas Esféricas

Gradiente em Coordenadas Parabolicas


Converted by Mathematica      April 26, 2001