3-Dimensional Position and Motion: Difference between revisions
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===A Mathematical Model=== | ===A Mathematical Model=== | ||
What are the mathematical equations that allow us to model this topic. For example <math><{\frac{d\vec{x}}{dt}},{\frac{d\vec{y}}{dt}},{\frac{d\vec{z}}{dt}}></math> is the velocity and <math> | What are the mathematical equations that allow us to model this topic. For example <math><{\frac{d\vec{x}}{dt}},{\frac{d\vec{y}}{dt}},{\frac{d\vec{z}}{dt}}></math> is the velocity and <math>{\frac{d\vec{(velocity)}}{dt}}</math> is the acceleration. | ||
===A Computational Model=== | ===A Computational Model=== | ||
Revision as of 20:53, 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.
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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.
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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.