3-Dimensional Position and Motion: Difference between revisions
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===Simple=== | ===Simple=== | ||
obj. is at position (0,0,0) meters, moving at a velocity of (-1, 4, 9) meters per second for n seconds. What is obj.'s position now? | |||
(0-n,0+4n,0+9n)=(-n,4n,9n) | |||
===Middling=== | ===Middling=== | ||
===Difficult=== | ===Difficult=== | ||
Revision as of 21:37, 5 December 2015
In order to be able to calculate the effect of forces on an object, you need to first be able to describe its position and motion in three dimensional space. For locating entities, we have position vectors. The change in position over time creates the velocity vector, which describes motion in space. From here, we can apply three dimensional forces.
The Main Idea
Objects, exist, move and accelerate in three dimensions, so we have to describe them in three dimensions as well.
A Mathematical Model
What are the mathematical equations that allow us to model this topic. For example [math]\displaystyle{ \lt {\frac{d\vec{x}}{dt}},{\frac{d\vec{y}}{dt}},{\frac{d\vec{z}}{dt}}\gt }[/math] is the velocity and [math]\displaystyle{ {\frac{d\vec{(velocity)}}{dt}} }[/math] is the acceleration.
A Computational Model
To program the position in VPython for an object, obj, write obj.pos=(xp,yp,zp). Here xp, yp, and zp are the x, y, and z coordinates, respectively, of the object. Velocity and acceleration are programmed similarly with obj.velocity=(xv,yv,zv) and obj.acceleration=(xa,ya,za). The x, y, and z velocity and acceleration values are xv, yv, and zv and xa, ya, and za respectively.
Examples
Here are a few examples
Simple
obj. is at position (0,0,0) meters, moving at a velocity of (-1, 4, 9) meters per second for n seconds. What is obj.'s position now? (0-n,0+4n,0+9n)=(-n,4n,9n)
Middling
Difficult
Connectedness
- How is this topic connected to something that you are interested in?
- How is it connected to your major?
- Is there an interesting industrial application?
History
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.
See also
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?
Further reading
Books, Articles or other print media on this topic
External links
References
This section contains the the references you used while writing this page
A Mathematical Model
To program the position in VPython for an object, obj, write obj.pos=(xp,yp,zp). Here xp, yp, and zp are the x, y, and z coordinates, respectively, of the object. Velocity and acceleration are programmed similarly with obj.velocity=(xv,yv,zv) and obj.acceleration=(xa,ya,za). The x, y, and z velocity and acceleration values are xv, yv, and zv and xa, ya, and za respectively.