Question

Question to Galactic Dynamics by James Binney and Scott Tremaine, 2nd edition

Problem 2: Coordinate transformations a) Derive the expressions for the divergence of a vector function Vf and the laplacian V2f of a scalar function f.

Answer 1

In quastim you do not SPecn Co-andinate, in Cantesian, Sphunical amd So I dona Co-aadinale Lin daical Now Cusuiineon coondinale taanskosmation Now Use ug In Cantesiam Co-oa dinade hi = h = hg - 1 Uz = 7 352 efe In Cylin daicol Corondinate d = ,=? , u2 = P

In Sphanical co-ondinode Now u, 3 9, Из-Ф виsd tч с а— ty вf -tf Sin h Sin 8 (+9 Now hih2h3 hah 43 In Cantesian U3 = 1 325 2 S2 - 2 n daical In Из -7 U2 — Ф) у hз I Nou + Зe 72

In SphaniCal Cosndinate u3. h3