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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 19 "File:  CONSERVE.mws" }}
{PARA 0 "" 0 "" {TEXT -1 30 "Software:  Maple V Release 4.0" }}{PARA 
0 "" 0 "" {TEXT -1 41 "Authors:    Perry Peters and Greg Williby" }}
{PARA 0 "" 0 "" {TEXT -1 37 "Concepts Used:  Spherical coordinates" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 13 "with(linalg):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
26 "Enter in the force vector." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "F
:=vector([x*y*z^3,x^2*z^3/2,3*x^2*y*z^2/2]);" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 39 "Show that the potential energy of F is:" }}{PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 16 "U:=-x^2*y*z^3/2;" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 79 "Perform partial derivative tests on U to see if it is the
 potential energy of F" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "dUdx:=-di
ff(U,x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "dUdy:=-diff(U,y
);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "dUdz:=-diff(U,z);" }}
}{EXCHG {PARA 0 "" 0 "" {TEXT -1 36 "U is thus the potential energy of
 F." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 35 "Co
nvert the vector into polar form." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
87 "sub1:=subs(\{x=rho*sin(phi)*cos(theta),y=rho*sin(phi)*sin(theta),z
=rho*cos(phi)\},op(F));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 20 "Direction of travel." }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 38 "P:=vector([-sin(theta),cos(theta),0]);" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 71 "Take the dot product of the force and the
 direction before integrating." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "F
cir:=dotprod(sub1,P);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 26 "Integrat
e around the loop." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "Int(Fcir,thet
a=0..2*Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "int(Fcir,the
ta=0..2*Pi);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 105 "This shows that \+
the work done on the particle around the loop for any constant value o
f phi and rho is 0." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "
0 0 0" 17 }{VIEWOPTS 1 1 0 1 1 1803 }