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183_notes:iterativepredict [2021/02/04 23:33] – [Predicting Motion Iteratively] stumptyl | 183_notes:iterativepredict [2021/02/04 23:35] – [Applying Iterative Prediction] stumptyl | ||
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To predict motion iteratively is to apply the [[183_notes: | To predict motion iteratively is to apply the [[183_notes: | ||
- | * Calculate the (vector) forces acting on the system. | + | *1.) - |
- | * Update the momentum of the system: $\vec{p}_f = \vec{p}_i + \vec{F}_{net}\Delta t$. | + | *2.) - Update the momentum of the system: $\vec{p}_f = \vec{p}_i + \vec{F}_{net}\Delta t$. |
- | * Update the position of the system: $\vec{r}_f = \vec{r}_i + \vec{v}_{avg}\Delta t$. | + | *3.) - Update the position of the system: $\vec{r}_f = \vec{r}_i + \vec{v}_{avg}\Delta t$. |
- | * Repeat | + | *4.) - Repeat |
- | This process can be used for any system with any type of force. The accuracy of your predictions depend on the length of the time step. By using this method, you assume that the net force and average velocity are roughly constant over the time interval (for each time interval). If you are interested in more details, this method is similar to [[http:// | + | This process can be used for any system with any type of force. The accuracy of your predictions depend on the length of the time step. __//By using this method, you assume that the net force and average velocity are roughly constant over the time interval (for each time interval).//__ If you are interested in more details, this method is similar to [[http:// |
==== Applying Iterative Prediction ==== | ==== Applying Iterative Prediction ==== | ||
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{{ 183_notes: | {{ 183_notes: | ||
- | If you were to connect the straight lines in this picture, you would see a trajectory that looks more like moving through a curved trajectory. The time step here is quite long for the motion, but using a shorter time step, the line segments are shorter and more closely produce a curved trajectory. | + | If you were to connect the straight lines in this picture, you would see a trajectory that looks more like moving through a curved trajectory. |
+ | // | ||
===== Examples ===== | ===== Examples ===== | ||
[[: | [[: |