This preview shows page 1. Sign up to view the full content.
Unformatted text preview: U =GMm r (77) and in our case of the particle U ( x, , 0) =GMm axGMm a + x =2 amMG a 2x 2 (78) Dierentiating gives U x =2 amMG [( a 2x 2 )2 (2 x )] =4 amMGx ( a 2x 2 ) 2 (79) indeed this is zero when x = 0. Dierentiating again: 2 U x 2 =4 amMG ( a 2x 2 ) 216 amMGx 2 ( a 2x 2 ) 3 (80) and evaluate at x = 0: 2 U x 2 =4 mMG a 3 (81) which indicates unstable equilibrium. 11...
View
Full
Document
This note was uploaded on 09/20/2010 for the course AMATH 261 taught by Professor Rogermelko during the Spring '10 term at Waterloo.
 Spring '10
 RogerMelko

Click to edit the document details