Updating force, momentum, and position: Difference between revisions
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===A Mathematical Model=== | ===A Mathematical Model=== | ||
The mathematical models we will use are force update equations, momentum update equations, and position update equations. | |||
Force (These equations are the force equations for whatever type of problem you are solving. In our case, the gravitational force of Earth on the Spacecraft.): | |||
<math>\vec{F}_{grav} = -G\frac{{m}_{earth}{m}_{craft}}{\abs{{r}_{earth \rightarrow craft}}^2}{\hat{r}}_{earth \rightarrow craft}</math> | |||
What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings. | What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings. | ||
Revision as of 21:56, 18 November 2015
This topic covers building a VPython script to loop until a specified time and update the fore, momentum, and position in a system to create a neat animation and solve problems dealing with force, momentum, and position at a specific time.
The Main Idea
The main idea is to take the mathematical models we already know, and learning the syntax to put them into a VPython script that can help us solve problems quickly and easily.
A Mathematical Model
The mathematical models we will use are force update equations, momentum update equations, and position update equations.
Force (These equations are the force equations for whatever type of problem you are solving. In our case, the gravitational force of Earth on the Spacecraft.): [math]\displaystyle{ \vec{F}_{grav} = -G\frac{{m}_{earth}{m}_{craft}}{\abs{{r}_{earth \rightarrow craft}}^2}{\hat{r}}_{earth \rightarrow craft} }[/math] What are the mathematical equations that allow us to model this topic. For example [math]\displaystyle{ {\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net} }[/math] where p is the momentum of the system and F is the net force from the surroundings.
A Computational Model
How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript
Examples
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Simple
Middling
Difficult
Connectedness
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History
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See also
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