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krsbuilt

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- Thread starter krsbuilt
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In summary: Remember that the relative speed between the two objects is the same before and after the collisions, making this simpler).In summary, elastic collisions are basically trading momentum between two colliding bodies.

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krsbuilt

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BruceW

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(Elastic collision means that momentum in all 3 directions is conserved, and energy is conserved).

For two solid objects, the direction they get scattered in depends on the shape of the objects and the relative angle between the objects before they collide.

For hard spheres (like pool balls), the direction that the two balls scatter is the normal to the small area where the two balls touch. (That sounds dirty).

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krsbuilt

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Edit: any elastic collision as an elastic collision between spheres

Edit 2: if the shapes are weird and the angles are off

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BruceW

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krsbuilt said:

Yes, If you think about it, the contact force between the two objects is at the point where they touch, and the direction of these forces is to stop the two objects from going into each other at that point.

To do a true simulation of two many-sides objects, you would need to calculate where each of the faces were and check to see if collision happened between any of the faces of one object with any of the faces of the other object. Then when the objects collide, you'd need to calculate the angles between these faces to calculate the direction of the force.

krsbuilt said:

Edit: any elastic collision as an elastic collision between spheres

Edit 2: if the shapes are weird and the angles are off

It wouldn't be realistic, but it would probably look fairly realistic.

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krsbuilt

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P.S. i apologize if that is hard to read, I'm kind of scatter-brained

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BruceW

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So let's say face

In actual collisions, the objects will squash a bit, and then spring back (imagine a tennis ball being hit by a racquet). So the value of the force, and the length of time it acts will depend on the material. In your simulation, I advise you just use values for these which make the simulation look fairly real. (I think a small time, with a fairly large force would look most realistic).

Now you have the force, its direction and how long it acts. The change in momentum is equal to the force times the time, so this gives you the change in momentum.

The component of the force pointing to the centre of gravity of the object contributes to the change in linear momentum.

The component of the force pointing at right-angles to the centre of gravity gives the change in angular momentum of the object. The angular momentum (assuming the object is roughly spherical) is equal to [itex] m 2 \pi f r^2 [/itex] In this equation, m is the mass of the object, f is the frequency of rotation of the object. And r is the radius at which the force happened (in our case, it will be distance from the centre of gravity to the point of corner

Hope this helped, its actually a pretty complicated simulation to make, now that I've thought about it.

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krsbuilt

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BruceW

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(This is because for a collision to happen where two planes were touching, the angle of these two planes would need to be perfectly aligned, which doesn't happen).

If you've got a plane which satisfies the equation ax+by+cz=d then (a,b,c) is the normal vector to that plane. To get the unit vector normal to the plane, you make it so that [itex] a^2 + b^2 + c^2 = 1 [/itex]. The unit vector normal to the plane is more useful in this case, because it equals the direction of the force.

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BruceW

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No, once you calculate each of them, they are independent things.

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BruceW

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1) the angular motion of the object about an axis through its centre of gravity (angular momentum).

and 2) the motion of the centre of gravity of the entire body (linear momentum).

So the full motion of a particular part of the body is the combination of 1) and 2).

(These are not the general meanings of the two terms, but in this case, these two definitions will do).

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krsbuilt

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BruceW

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The angular momentum of one object is exactly opposite to the angular momentum of the other object.

Therefore, the angular momentum was zero before collision and is zero after collision.

An elastic collision in three dimensions is a type of collision between two objects where both the momentum and kinetic energy are conserved. This means that the total momentum and total kinetic energy before the collision is equal to the total momentum and total kinetic energy after the collision.

The conditions for an elastic collision in three dimensions are that there are no external forces acting on the objects, the objects must be rigid and not deform during the collision, and the collision must be head-on.

The velocity of each object after an elastic collision in three dimensions can be calculated using the conservation of momentum and kinetic energy equations. The equations take into account the masses and velocities of the objects before and after the collision.

Yes, an elastic collision in three dimensions can occur between more than two objects as long as all the conditions for an elastic collision are met. The conservation of momentum and kinetic energy equations become more complex with more objects involved.

Some real-world examples of elastic collisions in three dimensions include collisions between gas particles in a closed container, collisions between billiard balls on a pool table, and collisions between molecules in a chemical reaction. These collisions demonstrate the principles of conservation of momentum and kinetic energy in three dimensions.

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