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--- 183_notes:iterativepredict [2018/05/29 20:06] – hallstein
+++ 183_notes:iterativepredict [2021/02/04 23:35] – [Applying Iterative Prediction] stumptyl
@@ Line 1: / Line 1: @@
-Section 2.3 and 2.4 in Matter and Interactions (4th edition)
+Section 2.3, 2.4 and 2.7 in Matter and Interactions (4th edition)
 ===== Predicting Motion Iteratively =====
-You read earlier [[183_notes:constantf|how to predict the motion of a system that experiences a constant force]]. However, **very few real systems can be approximately modeled using constant force motion**.
+You read earlier [[183_notes:constantf|how to predict the motion of a system that experiences a constant force]]. //However, very few real systems can be approximately modeled using constant force motion.//
 All systems can be modeled iteratively, that is, applying the motion prediction tools ([[183_notes:motionpredict|momentum update]] and [[183_notes:displacement_and_velocity|position update]]) in repeated small steps. In these notes, you will read about this iterative process and how it is related to formal calculus.
@@ 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 ====
@@ Line 30: / Line 30: @@
 {{ 183_notes:mi3e_02-019.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]]