{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 256 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 } {PSTYLE "Normal" -1 257 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 1 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 258 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 259 1 {CSTYLE "" -1 -1 "T imes" 1 18 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 } } {SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT 256 47 "Trajectories in an Attr active Central Potential" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 257 "" 0 "" {TEXT -1 48 "by Jason Janesky, Corinne Manogue & Kerry Browne " }}{PARA 258 "" 0 "" {TEXT -1 30 "Copyright 2007 Corinne Manogue" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 258 "" 0 "" {TEXT -1 53 "This wo rksheet calculates the trajectories of a mass " }{XPPEDIT 18 0 "mu" "6 #%#muG" }{TEXT -1 52 " under the influence of a CENTRAL force numerica lly." }}{PARA 258 "" 0 "" {TEXT -1 103 "The main example of a central \+ force which we've been studying in class is an attractive inverse squa re:" }}{PARA 256 "" 0 "" {XPPEDIT 18 0 "f(r)=-k/r^2" "6#/-%\"fG6#%\"rG ,$*&%\"kG\"\"\"*$F'\"\"#!\"\"F." }}{PARA 258 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 258 "> " 0 "" {MPLTEXT 1 0 53 "restart:with(DEtools):with (plots):\nplotsetup(window):" }}}{EXCHG {PARA 258 "" 0 "" {TEXT -1 0 " " }{TEXT 257 18 "Setup the Problem\n" }{TEXT -1 43 "Choose values for \+ the parameters below: " }}{PARA 258 "" 0 "" {TEXT -1 0 "" }}{PARA 258 "" 0 "" {TEXT -1 60 "The masses of each of the particles and the r educed mass are" }}{PARA 258 "> " 0 "" {MPLTEXT 1 0 33 "m1:=2; m2:=2; \+ mu:= m1*m2/(m1+m2);" }}}{EXCHG {PARA 258 "" 0 "" {TEXT -1 63 "\nThe an gular momentum, total energy, and coupling constant are:" }}}{EXCHG {PARA 258 "> " 0 "" {MPLTEXT 1 0 21 "el:=1; E:= -.2; k:=1;" }}}{EXCHG {PARA 258 "" 0 "" {TEXT -1 0 "" }}{PARA 258 "" 0 "" {TEXT -1 50 "The c entral potential and effective potential are:" }}}{EXCHG {PARA 258 "> \+ " 0 "" {MPLTEXT 1 0 8 "U:=-k/r;" }}}{EXCHG {PARA 258 "> " 0 "" {MPLTEXT 1 0 24 "Veff:=U+el^2/(2*mu*r^2);" }{TEXT -1 0 "" }}}{EXCHG {PARA 258 "> " 0 "" {MPLTEXT 1 0 51 "plot([Veff,E],r=0..4,-2..3,\ncolo r=[magenta,green]);" }}}{EXCHG {PARA 258 "" 0 "" {TEXT -1 77 "\nWhat t ype of orbit would you guess for these parameters? What do you think \+ " }{XPPEDIT 18 0 "r[min]" "6#&%\"rG6#%$minG" }{TEXT -1 5 " and " } {XPPEDIT 18 0 "r[max]" "6#&%\"rG6#%$maxG" }{TEXT -1 9 " will be?" }}}} {MARK "1 0 0" 53 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }