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F ma<br />
linear momentum p mv<br />
F d p dt<br />
particle kinetic energy T 1 2 mv2<br />
I<br />
angular momentum H I cg <br />
d<br />
dt H<br />
rigid body T 1 Mv 2 cg<br />
2 1 I 2<br />
2<br />
cg<br />
my 2 n y n 2 y fy,t<br />
y cy k m y fy,t<br />
n <br />
For small<br />
epsilon<br />
1<br />
1<br />
1<br />
1<br />
1 <br />
1 <br />
k<br />
m ,c 2 n<br />
m<br />
conservation of angular momentum d dt<br />
H constant<br />
x n2 x 0<br />
If n 0 then sinusodial solution, ok<br />
if n 0 then solution blows up, exponential<br />
52
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