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
;
Print
@
"Kinematics"
D
;
m
=
2;
L
=
1;
g
=
9.81;
k
=
2000;
alpha
=
8
0,0,theta''
@
t
D<
;
Print
@
"angular acceleration of RB: alpha
=
",alpha
D
;
xC
=
H
L 2
L
*
Cos
@
theta
@
t
DD
;
yC
=
H
L 2
L
*
Sin
@
theta
@
t
DD
;
rC
=
8
xC,yC,0
<
;
Print
@
"position vector of C: rC
=
",rC
D
;
xA
=
L
*
Cos
@
theta
@
t
DD
;
yA
=
L
*
Sin
@
theta
@
t
DD
;
rA
=
8
xA,yA,0
<
;
Print
@
"position vector of A: rA
=
",rA
D
;
Print
@
"Forces"
D
;
G
=
8
0,

mg,0
<
;
Print
@
"gravitational force at C: G
=
", G
D
;
delta
=
LSin
@
theta
@
t
DD

LSin
@
Pi 6
D
;
Fe
=
8
0,

kdelta,0
<
;
Print
@
"elastic force at A: Fe
=
", Fe
D
IC
=
m
*
L^2 12;
Print
@
"mass moment of inertia wrt C: ICz
=
",IC
D
;
IO
=
IC
+
m
*
H
L 2
L
^2;
Print
@
"mass moment of inertia wrt O: IOz
=
ICz
+
m
*
H
L 2
L
^2
=
",
Simplify
@
IO
DD
;
Print
@
"Summ of the moments in O at t
>
t1:"
D
eqI
=
Simplify
@
IO
*
alpha

Cross
@
rC,G
[email protected]@
3
DD
;
solutionI
=
Solve
@
eqI 0,theta''
@
t
[email protected]@
1
DD
;
Print
@
"moment equation: IO alpha
=
sum M wrt O
=
rC x G"
D
;
Print
@
"Solution: theta''
@
t
D
=
",theta''
@
t
D
.Simplify
@
solutionI
DD
;
H
**
L
t0
=
0;
soldif
=
NDSolve
@8
eqI 0, theta
@
0
D
==
N
@
Pi
D
3, theta'
@
0
D
==
0
<
,theta,
8
t,t0,Infinity
<
,
Method
fi
8
EventLocator, "Event"
fi
H
theta
@
t
D

Pi 6
L<D
;
t1
=
InterpolatingFunctionDomain
@
First
@
theta . soldif
[email protected]@
1,

1
DD
;
theta1
=
H
Evaluate
@
theta
@
t
D
. soldif
D
. t
fi
t1
[email protected]@
1
DD
;
omega1
=
H
Evaluate
@
D
@
theta
@
t
D
.soldif,t
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 Fall '11
 Marghitu
 Moment Of Inertia, 1 , thetam, deltam, 0.0650279 m

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