How Do You Calculate Resulting Velocity Vectors in 3D Collisions?

[MinatureCook]

Hey, I've done quite a bit of Mechanics work in the past... But I really don't even know where to start here.

For some work I'm doing, I need to calculate the resulting velocity vectors when 2 objects collide. These 2 objects can be any shape, any mass and going at any velocity independently. (The simulation is in 3D, so x, y, z)

I suppose I'd have to calculate the normal of the two objects, do something with their velocity vectors and masses... And I suppose it would also depend on the objects' bounciness/stiffness etc...

If anyone could give me the names of some equations I can look into? Or any sort of help... Really just a place to start would be great.

Thanks for any help,
Stephen

 

[AJ Bentley]

Commonly called a Billiard ball collision.

 

[MinatureCook]

I'm Googling that term now, apparently it's also called "Elastic Collision" which is a great help (I had no idea of what to even start searching before) - but all of the equations seem to be confined to a 1D plane of movement.

Would it just be a matter of making the velocity vectors 3D? Here's to hoping so - it's just things rarely are so simple when transferring over to 3 dimensions in Maths

Edit:
Ahh, actually - I just found this Wikipedia article
http://en.wikipedia.org/wiki/Elastic_collision
Which explains about 2D and 3D at the bottom. It's not as simple, but neither is it beyond my knowledge - so I'm happy there :P

Thanks a lot for the help; I genuinely wouldn't have known where to start looking without that

 

[AJ Bentley]

Perfectly OK to just go to 3 dimensions. Or as many as you like ;-)

You just have to resolve the velocities and momenta into 3 orthogonal directions.

Of course, you rarely have to do that in physics problems because any collision between two particles is only in 1 plane, even when it's a glancing collision.

You might want to consider inelastic collision - in the real world things tend to splat more than they bounce.

If it's not a serious project ( a game for example) you could equally well 'fake it'. Just use random direction changes and keep the total momentum/ energy constant (or lose a bit - inelastic). No need to meticulously work out contact angles.

 

[PJC01]

I can provide some guidance on how to approach this problem. First, it is important to understand the principles of momentum and collision in 3D. Momentum is a property of a moving object and is defined as the product of its mass and velocity. In a collision, the total momentum of the system before the collision is equal to the total momentum after the collision, assuming there are no external forces acting on the system. This is known as the law of conservation of momentum.

To calculate the resulting velocity vectors after a collision, you would need to use the momentum equation, which states that the initial momentum (mass x initial velocity) of an object is equal to its final momentum (mass x final velocity). In 3D, this equation would need to be applied to all three components (x, y, z) separately.

In terms of the objects' shapes, masses, and velocities, you would need to consider the principle of impulse, which is the change in momentum of an object over a period of time. This can be calculated by multiplying the force applied to an object by the time it is applied. In a collision, the impulse is equal to the force applied during the collision multiplied by the time it takes for the collision to occur.

To determine the resulting velocity vectors, you would need to use the principles of conservation of momentum and impulse, along with the objects' masses, velocities, and stiffness, to solve for the final velocities. This can be done using vector algebra and trigonometry.

Some equations that may be useful in this problem are the impulse-momentum equation, the law of conservation of momentum, and the equations for calculating the final velocities in a 3D collision.

I recommend researching these equations and principles further and consulting with a physics textbook or a qualified expert for more specific guidance on your particular problem. Good luck with your work, Stephen!