gibson:teaching:fall-2013:math445:lecture21
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gibson:teaching:fall-2013:math445:lecture21 [2013/12/03 05:48] gibson created |
gibson:teaching:fall-2013:math445:lecture21 [2013/12/03 05:50] (current) gibson [Physics] |
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| Pendulum physics, F = ma with linear air resistance | Pendulum physics, F = ma with linear air resistance | ||
| - | m l theta'' = -mg sin theta - b theta' | + | <latex> |
| + | m l \theta'' = -mg sin \theta - b \theta' | ||
| - | theta'' + c theta' + g/l sin theta = 0 | + | \theta'' + c \theta' + g/l \sin \theta = 0 |
| + | </latex> | ||
| This is a 2nd-order nonlinear differential equation in one variable, theta. | This is a 2nd-order nonlinear differential equation in one variable, theta. | ||
| - | 2nd order b/c theta'' term. Nonlinear b/c sin theta. Linearization for small | + | 2nd order b/c $\theta''$ term. Nonlinear b/c $\sin \theta$. Linearization for small |
| - | theta would approximate sin theta = theta for small theta. No big thing | + | theta would approximate sin theta = theta for small $\theta$. No big thing |
| =====Get ODE into Matlab form===== | =====Get ODE into Matlab form===== | ||
| Line 29: | Line 31: | ||
| to a 1st order ODE in n variables, as follows. Let | to a 1st order ODE in n variables, as follows. Let | ||
| + | <latex> | ||
| x1 = theta | x1 = theta | ||
| x2 = theta' | x2 = theta' | ||
| + | </latex> | ||
| Then | Then | ||
gibson/teaching/fall-2013/math445/lecture21.1386078488.txt.gz · Last modified: 2013/12/03 05:48 by gibson
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