chapter 4 lyapunov stability -...
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Chapter 4Lyapunov Stability
Example: The Pendulum
Example : The Pendulum(1)
1 2
2 2 12
1 1 2 21 2
1 2 1 2
* *1 2
2
22
sin
0, 1, cos ,
0 10, 0,
0
x xb gx x x
MR Rf f f fg bxx x x R x MR
x x A g bR MR
b gs sMR R
Example: The Pendulum(2)
* *1 2
2
22
*1 1 1 1 2 2
1 2
2 2 12
0 1, 0,
0
,
sin( )
x x A g bR MR
b gs sMR R
z x x x z xz z
b gz z zMR R
Example
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