Physics:2D Physics Engine:Springs

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Introduction
Collision Detection
Rigid Bodies
Extra 'stuff'
- Information Packets
- Segment Collision Detection
- Springs
- Joints
Conclusion

1 Explanation
2 Description

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Explanation

A spring is a connection between two objects that will use impulses to put it back to the correct position instead of constraining it.

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Description

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Hooke's Law

Hooke's Law states that the the force to move two objects together with a spring is proportional to the distance apart, or

$\vec{F}$ : Force vector to restore the objects to the correct position
$k$ : Spring constant, a number describing how fast the objects will move to get to the correct position
$\vec{x}$ : A vector equal to the difference in position of the two bodies' positions

$\vec{F} = -k\vec{x}$

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Hooke's Law with Damping

Using the plain version of Hooke's Law will cause the spring to oscillate forever. However, a modified version with damping causes the objects eventually stop.

$\vec{F}$ : Force vector to restore the objects to the correct position
$k$ : Spring constant, a number describing how fast the objects will move to get to the correct position
$\vec{x}$ : A vector equal to the difference in position of the two bodies' positions
$\vec{v}$ : A vector equal to the difference in velocity of the two bodies
$b$ : Damping constant, a number describing how quickly the objects will slow to a stop. Negative values will cause the objects to accelerate

$\vec{F} = -k\vec{x} - b\vec{v}$

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Alternate Spring Equations

There are more possible equations than Hooke's Law. A rather useful one keeps the bodies a certain distance apart.

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Length Spring

This type of spring will keep the two objects a certain distance apart.

$\vec{F}$ : Force vector to restore the objects to the correct position
$k$ : Spring constant, a number describing how fast the objects will move to get to the correct position
$\vec{x}$ : A vector equal to the difference in position of the two bodies' positions
$|\vec{x}|$ : The magnitude of $\vec{x}$
$d$ : The distance to keep the bodies apart (the desired length of the spring)
$\vec{v}$ : A vector equal to the difference in velocity of the two bodies
$b$ : Damping constant, a number describing how quickly the objects will slow to a stop. Negative values will cause the objects to accelerate