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

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    3d Collision Momentum
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Discussion Overview

The discussion revolves around calculating resulting velocity vectors in 3D collisions between two objects of varying shapes, masses, and velocities. Participants explore the theoretical and practical aspects of collision mechanics, including elastic and inelastic collisions.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant, Stephen, seeks guidance on calculating resulting velocity vectors in 3D collisions and mentions the need to consider the normal of the objects, their velocities, masses, and properties like bounciness.
  • Another participant refers to the scenario as a "Billiard ball collision," suggesting a common terminology for such interactions.
  • Stephen discovers that the term "Elastic Collision" is relevant and notes that existing equations are primarily for 1D scenarios, questioning the adaptation to 3D.
  • A later reply confirms that it is acceptable to extend calculations to 3 dimensions by resolving velocities and momenta into orthogonal directions, while noting that many physics problems simplify to 1D planes even in glancing collisions.
  • Participants discuss the possibility of considering inelastic collisions, suggesting that real-world interactions often result in splattering rather than bouncing.
  • One participant proposes a simplified approach for non-serious projects, suggesting the use of random direction changes while maintaining total momentum or energy, rather than calculating precise contact angles.

Areas of Agreement / Disagreement

There is no consensus on a single method for calculating resulting velocity vectors in 3D collisions, as participants present various approaches and considerations, including both elastic and inelastic collisions.

Contextual Notes

Participants express uncertainty regarding the complexity of adapting 1D collision equations to 3D scenarios and the implications of different collision types on the calculations.

MinatureCook
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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
 
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Commonly called a Billiard ball collision.
 
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 :rolleyes:

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
 
Last edited:
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.
 

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