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| − | == Basic concepts ==
| + | * [[Darwinbots3/Physics/Response | Collision Response]] - Article covers math behind responding to collisions |
| − | | + | * [[Darwinbots3/Physics/Detection | Collision Detection]] - Article covers methods of broad and narrow phase collision detection for simple 2D shapes |
| − | === Forces' linear affects ===
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| − | 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:
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| − | __________
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| − | | X | <--- <math>\vec{Force_1}</math>
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| − | |________| <--- <math>\vec{Force_2}</math>
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| − | ''' Diagram 1 '''
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| − | Where X is the center of mass for the body. <math>\vec{Force_1}</math> is exactly centered, so it produces no torque. The change in acceleration of the body's center of mass is given by <math>\Delta \vec{a} = \frac{\vec{Force_1}}{Mass}</math>.
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| − | Let <math>\vec{Force_2}</math> have the same magnitude and direction as <math>\vec{Force_1}</math>. 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 <math>\Delta \vec{a} = \frac{\vec{Force_1}}{Mass}</math>.
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| − | === Forces' angular affects ===
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| − | Consider Diagram 1 again. <math>\vec{Force_1}</math> will not produce any change in angular acceleration for the body, because it is centered. <math>\vec{Force_2}</math> ''will'' produce change in angular acceleration, because it is off center. In general, the '''torque''' (<math>\tau</math>) produced by a force is given by:
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| − | :<math>\tau = \vec{F} \cdot \vec{r_{\perp}^{P}}</math>
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| − | And the change in angular acceleration is given by:
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| − | :<math>\Delta \alpha = \frac{\tau}{I}</math>
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| − | Where:
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| − | * <math>\tau</math> is the scalar torque term.
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| − | * <math>\vec{F}</math> is the vector Force term.
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| − | * <math>\vec{r_{\perp}^{P}}</math> is the vector perpendicular to the vector from the body's origin to the place <math>\vec{F}</math> is acting on the body.
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| − | * <math>\alpha</math> is the scalar angular acceleration | |
| − | * <math>I</math> is the body's scalar moment of inertertia.
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| − | == Collision ==
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| − | Consider a collision between two bodies: body A and body B. It is possible to [http://chrishecker.com/images/e/e7/Gdmphys3.pdf show] that the [http://en.wikipedia.org/wiki/Impulse impulse] from the collision is given by the solution to:
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| − | :<math>
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