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In[724]:=
H
*
packages that have some differential
equations to solve and define some utility functions
*
L
Needs
@
"DifferentialEquations`NDSolveProblems`"
D
;
Needs
@
"DifferentialEquations`NDSolveUtilities`"
D
;
Needs
@
"DifferentialEquations`InterpolatingFunctionAnatomy`"
D
;
Needs
@
"GUIKit`"
D
;
ClearAll
@
"Global`
*
"
D
;
Off
@
General::
spell
D
;
Off
@
General::
spell1
D
;
R
=
0.01;
V
=
4 Pi R^3
ê
3;
m
=
0.0327;
E1
=
200
*
10^9;
Sy
=
1.12
*
10^9;
nu
=
0.33;
Ep
=
HH
1

nu^2
Lê
E1
+
H
1

nu^2
Lê
E1
L
^

1;
k1
=
2
3
H
1

nu^2
L
E1
R ;
g
=
9.81;
h
=
0.1;
v0
=
Sqrt
@
2 g h
D
;
H
=
3 Sy;
H
*
Chang
*
L
K
=
0.454
+
0.41 nu;
xc
=
H
Pi K H
êH
2 Ep
LL
^2 R;
H
*
Jackson
*
L
CJ
=
1.295 E^
H
0.736 nu
L
;
xcJ
=
H
Pi CJ Sy
êH
2 Ep
LL
^2 R;
Print
@
"Chang: xc
=
", xc, "
@
m
D
"
D
Print
@
"Jackson: xc
=
", xcJ, "
@
m
D
"
D
H
*
m x''
@
t
D
==
m g

k1 x
@
t
D
^
H
3.
ê
2
L
*
L
eq
=
m x''
@
t
D
==
m g

k1
H
x
@
t
DL
^
H
3.
ê
2
L
;
Print
@
" "
D
Print
@
"Chang"
D
;
solC
=
NDSolve
@8
eq, x
@
0
D
ã
0, x'
@
0
D
ã
v0
<
, x,
8
t, 0, Infinity
<
,
Method
Ø
8
EventLocator, "Event"
Ø
H
x
@
t
D

1.9 xc
L<D
;
tIC
=
InterpolatingFunctionDomain
@
First
@
x
ê
. solC
DD@@
1,

1
DD
;
xIC
=
Chop
@
First
@
Evaluate
@
x
@
t
D ê
. solC
D ê
. t
Ø
tIC
DD
;
vIC
=
Chop
@
First
@
Evaluate
@
x'
@
t
D ê
. solC
D ê
. t
Ø
tIC
DD
;
Print
@
"tI
=
", tIC, "
@
s
D
"
D
;
Print
@
"xI
=
", xIC, "
@
m
D
"
D
;
Print
@
"vI
=
", vIC, "
@
m
ê
s
D
"
D
;
Print
@
" "
D
;
Print
@
"Jackson"
D
;
Print
@
" "
D
;
Print
@
"critical values "
D
;
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@
"xc
=
", xcJ, "
@
m
D
"
D
Pc
=
k1 xcJ^
H
3.
ê
2
L
;
Print
@
"Pc
=
k1 xc^
H
3.
ê
2
L
=
", Pc, "
@
N
D
"
D
;
PcJ
=
4.
ê
3
H
R
ê
Ep
L
^2
H
Pi CJ Sy
ê
2
L
^3;
Print
@
"Pc
=
4.
ê
3
H
R
ê
Ep
L
^2
H
Pi CJ Sy
ê
2
L
^3
=
", PcJ, "
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 Fall '11
 Marghitu

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