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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "restart;# stretch in
 members in terms of displs ux and uy of joint 2" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 50 "d12:=(ux+uy)/sqrt(2);d42:=uy;d23:=(ux-uy)/sqr
t(2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$d12G,$*(\"\"#!\"\",&%#uxG
\"\"\"%#uyGF+F+F'#F+F'F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$d42G%#u
yG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$d23G,$*(\"\"#!\"\",&%#uxG\"\"
\"%#uyGF(F+F'#F+F'F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 186 "#e
nergy V is PE in rods plus PE due to load. members 1 and 2 have stiffn
ess k=EA/L, member 3 has stiffness k2=EA/(L/sqrt(2))=sqrt(2)*k\nV:=(1/
2)*k*(d12^2+d23^2+sqrt(2)*d42^2)-p1*ux-p2*uy;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"VG,(*(\"\"#!\"\"%\"kG\"\"\",(*&F'F(,&%#uxGF*%#uyGF*
F'F**&F'F(,&F.F*F/F(F'F**&F'#F*F')F/F'F*F*F*F**&%#p1GF*F.F*F(*&%#p2GF*
F/F*F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "#eqns\nex:=diff(V
,ux);ey:=simplify(diff(V,uy));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#e
xG,&*&%\"kG\"\"\"%#uxGF(F(%#p1G!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#>%#eyG,(*&%\"kG\"\"\"%#uyGF(F(*(F'F(\"\"##F(F+F)F(F(%#p2G!\"\"" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "#matrix form\nK:=matrix([[k,
0],[sqrt(2)*k,k]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"KG-%'matrix
G6#7$7$%\"kG\"\"!7$*&F*\"\"\"\"\"##F.F/F*" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 23 "solve(\{ex,ey\},\{ux,uy\});" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#<$/%#uxG*&%#p1G\"\"\"%\"kG!\"\"/%#uyG*(%#p2GF(F)F*,&F(F
(*$\"\"##F(F1F(F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}
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