1q2H2q2q3H3q3
xrsi
cosHr1Hryrsi
si
zrcosHrsi
对于球坐标
ur
A
ur
u

1ur
u
1ursi

21rrsi
Arrsi
ArA2rsi
2
u
1rsi
2
2uuursi
rrsi
rrrsi
r
H1HrHz1
xcosysi
zz
对于柱坐标
u
u
u
1u
uz
uz
1AAAzAz
fu
1u1uuzz
§401拉普拉斯方程u
a在球坐标系中
1rsi
2
0
2uuursi
r0rsi
2rrrsi
r
设urRrY则
Ysi
d2RYRYirRs
drrsi
0
有
1d2dR1Y12Yrsi
ll1RdrdrYsi
si
2
d2dR1欧勒型方程ltdrrdrll1R0令eRrCrDrl1r22Y1si
Y1Yll1Y0si
dsi
dll1si
21dsi
si
22ddd2
2m2m012AcosmBcosr