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183_notes:iterativepredict [2015/09/03 16:02] – [Predicting Motion Iteratively] caballero | 183_notes:iterativepredict [2021/02/04 23:34] – [The Concept of Iterative Prediction] stumptyl | ||
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+ | Section 2.3, 2.4 and 2.7 in Matter and Interactions (4th edition) | ||
===== Predicting Motion Iteratively ===== | ===== Predicting Motion Iteratively ===== | ||
- | You read earlier [[183_notes: | + | You read earlier [[183_notes: |
All systems can be modeled iteratively, | All systems can be modeled iteratively, | ||
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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 ==== |