Iterative Prediction of Spring-Mass System: Difference between revisions
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The Momentum Principle provides a mathematical basis for the repeated calculations needed to predicts the system's future motion. | The Momentum Principle provides a mathematical basis for the repeated calculations needed to predicts the system's future motion. | ||
The most useful form of this equation is referred to as the "momentum update form" of the Momentum Principle | The most useful form of this equation is referred to as the "momentum update form" of the Momentum Principle, and can be derived as shown below: | ||
<math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> | <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> | ||
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<math>{\vec{p}_{f} = \vec{p}_{i} + \vec{F}_{net}{Δt}}</math> | <math>{\vec{p}_{f} = \vec{p}_{i} + \vec{F}_{net}{Δt}}</math> | ||
In order to update the object's velocity and position, similar equations can be used: | |||
<math>{\vec{v}_{f} = \vec{v}_{i} + \frac{\vec{F}_{net}}{m}}{Δt}</math> | |||
<math>{\vec{r}_{f} = \vec{r}_{i} + \vec{v}_{avg}{Δt}}</math></div> | |||
===A Computational Model=== | ===A Computational Model=== | ||
Revision as of 11:32, 1 December 2015
claimed by kgiles7
Short Description of Topic
The Main Idea
A simple spring-mass system is a basic illustration of the momentum principle. The principle of conservation of momentum can be repeatedly applied to predict the system's future motion.
A Mathematical Model
The Momentum Principle provides a mathematical basis for the repeated calculations needed to predicts the system's future motion.
The most useful form of this equation is referred to as the "momentum update form" of the Momentum Principle, and can be derived as shown below:
[math]\displaystyle{ {\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net} }[/math]
[math]\displaystyle{ {\vec{p}_{f} - \vec{p}_{i} = \vec{F}_{net}{Δt}} }[/math]
[math]\displaystyle{ {\vec{p}_{f} = \vec{p}_{i} + \vec{F}_{net}{Δt}} }[/math]
In order to update the object's velocity and position, similar equations can be used:
[math]\displaystyle{ {\vec{v}_{f} = \vec{v}_{i} + \frac{\vec{F}_{net}}{m}}{Δt} }[/math]
[math]\displaystyle{ {\vec{r}_{f} = \vec{r}_{i} + \vec{v}_{avg}{Δt}} }[/math]
A Computational Model
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