Physics 325 Spring 2011 Discussion 6 February 28, 2011 A particle of mass μ and initial angular momentum ‘ is moving in a central force ﬁeld F ( r ) = kr, with k >0 . Starting from the central force equation u 00 + u =-μ ‘ 2 u 2 F ± 1 u ² , where u0 = du/dθ and u = 1 /r , we want to solve for the particle’s path using the following steps. (a) If u0 = 0 at u = 1 /s , solve for ( u0 ) 2 as a function of u . Here, s is given by s = ± ‘ 2 μk ² 1 / 4 (b) Assuming u0 ≥0 , integrate once more to solve for u as a function of θ . Use initial condition r 2 sin α = s 2 at θ = 0 , for a given α . Hint: Make the substitution u 2 =
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This note was uploaded on 10/06/2011 for the course PHYS 325 taught by Professor Staff during the Spring '08 term at University of Illinois, Urbana Champaign.