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--- 183_notes:iterativepredict [2021/02/04 23:33] – [Predicting Motion Iteratively] stumptyl
+++ 183_notes:iterativepredict [2021/02/15 02:46] (current) – [Applying Iterative Prediction] stumptyl
@@ Line 18: / Line 18: @@
 To predict motion iteratively is to apply the [[183_notes:motionpredict|momentum update]] and [[183_notes:displacement_and_velocity|position update]] formula over small time steps, using their own predictions and the inputs for the next calculation. The steps for iteratively prediction motion are as follows:
-  * Calculate the (vector) forces acting on the system.
+  *1.) -  Calculate the (vector) forces acting on the system.
-  * 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://en.wikipedia.org/wiki/Semi-implicit_Euler_method|Euler-Cromer symplectic integration]].
+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://en.wikipedia.org/wiki/Semi-implicit_Euler_method|Euler-Cromer symplectic integration]].
 ==== Applying Iterative Prediction ====
 To reiterate, this method is not limited to non-constant forces and can be used to predict the motion in situations where a constant force model can be applied. A visual representation of such an iterative prediction over 3 steps is shown below. In each step, the momentum changes and, thus, the new momentum is calculated. This new momentum is used to determine the new location of the ball. The process is executed again with an updated prediction.
-{{ 183_notes:mi3e_02-019.png?400 }}
+{{ 183_notes:weektwo_iterative.png?400 }}
-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. //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.
+//
 ===== Examples =====
 [[:183_notes:examples:predicting_the_motion_of_system_subject_to_a_spring_interaction]]