Difference between revisions of "Darwinbots3/Physics"

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Revision as of 03:08, 28 April 2009

Basic concepts

Forces' linear affects

Any force acting on a body, at any point on a body, applies the same change in acceleration to the body's center of mass. Consider the diagram below: 

__________
|        |
|        |  
|   X    |  <--- \vec{Force_1}
|        |
|________|  <--- \vec{Force_2}
 Diagram 1

Where X is the center of mass for the body. \vec{Force_1} is exactly centered, so it produces no torque. The change in acceleration of the body's center of mass is given by \Delta \vec{a} = \frac{\vec{Force_1}}{Mass}.

Let \vec{Force_2} have the same magnitude and direction as \vec{Force_1}. However it's applying its force at a different point on the body, and will produce torque. Even though it's off center, the change in acceleration for the body's center of mass is still \Delta \vec{a} = \frac{\vec{Force_1}}{Mass}.

Forces' angular affects

Consider Diagram 1 again. \vec{Force_1} will not produce any change in angular acceleration for the body, because it is centered. \vec{Force_2} will produce change in angular acceleration, because it is off center. In general, the torque (\tau) produced by a force is given by:

\tau = \vec{F} \cdot \vec{r_{\perp}^{P}}

And the change in angular acceleration is given by:

\Delta \alpha = \frac{\tau}{I}

Where:

  • \tau is the scalar torque term.
  • \vec{F} is the vector Force term.
  • \vec{r_{\perp}^{P}} is the vector perpendicular to the vector from the body's origin to the place \vec{F} is acting on the body.
  • \alpha is the scalar angular acceleration
  • I is the body's scalar moment of inertertia.

Collision

Consider a collision between two bodies: body A and body B. It is possible to show that the impulse from the collision is given by the solution to:

<math>
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