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Colliding Ovals

  1. Mar 6, 2014 #1
    Hi,

    I Have set up 4 collisions between two Ovals (AA,BB,CC,DD) and I would like to know if the outcome will be identical for all 4 of them.

    First of, when looking at this orange collision that is going to take place, one can draw straight vertical lines between the two centers ...

    attachment.php?attachmentid=67307&stc=1&d=1394114608.png

    … and if you fly along with the lower oval, and draw it out; than it looks as if they are approaching each other in a straight line:

    attachment.php?attachmentid=67308&stc=1&d=1394114608.png

    Next, look at the 4 collisions (AA,BB,CC,DD) in the image below, than you can draw 4 times the same visual thing as the image above, when flying each time along with the lower Oval ABDC, be it for collision AA, BB, CC or DD.

    The right frame of reference to calculate collisions in is center of mass frame ... and when looking at this from a 'set' view from the top, than the outcome would be 4 x times different, but is it also 4 times different? ... cause they are all coming from different directions, and are differently orientated before they collide, and inertia-wise ... so my guess would be that the out comes are in fact also really different each time, although they approach each other visually in the same way.

    attachment.php?attachmentid=67310&stc=1&d=1394115793.png

    A friend gave me this explanation (see quote below), but it doesn't seem to be right ... so that's why I'm posting it here, just to be sure.

    Looking forward to hear your opinion(s), thanks!

    m.

     

    Attached Files:

  2. jcsd
  3. Mar 6, 2014 #2
    Your friend is right. The quote is correct
     
  4. Mar 6, 2014 #3
    But if you replace the 'mirrored' lower half with a flat plane than 'C' would be smacked onto that plane; while 'A' would 'shoot' straight through. So what's the difference with that?
     
  5. Mar 6, 2014 #4
    No, A would also reflect off the plane
     
  6. Mar 6, 2014 #5
    The one factor that might be different between the collisions is how fast the collision happens. But you did not mention that at all so I assume it is not important for that particular question.
     
  7. Mar 6, 2014 #6
    Mh, yes, the feeling I have is that 'C' is moving more powerful (faster?) in the Vertical direction vs. the Horizontal direction, and visa versa for 'A'. Let's say that they are all moving at the same speed towards the 'rendezvous point ' (black arrow).

    I'm adding an image to show what I meant with 'smack' vs. 'shoot through':

    attachment.php?attachmentid=67328&stc=1&d=1394127081.png
     

    Attached Files:

  8. Mar 6, 2014 #7
    Yes, if the magnitude of their speeds are all the same than the component of the speeds along the vertical will be different. That doesn't change the fact that it is best to model all these collisions in the center of mass frame. The collisions will all look the same except that some will happen faster than others. I'm assuming all the collisions conserve energy. If that's not the case than the different center-of mass-impact-speed might have an effect.
     
  9. Mar 6, 2014 #8
    So all 4 collisions (AA, BB, CC, DD) are different if V(black arrow)=1

    btw, they are all placed in a circle, so that should have indicated that they're all moving with V(black arrow)=1 towards the center of the collision. (It wasn't exactly so in the first image, so I've made a newer version where this is the case.)

    btw if (x,y) -> V(black arrow) ≠ 1 than I couldn't have made the illustration this way, and the distribution should be looking different, no?

    attachment.php?attachmentid=67332&stc=1&d=1394129813.png


    ok.

    Faster or slower ... now they all 'look the same', but what if V(black arrow) = 1

    Shouldn't they than not look the same?


    'might' that's a vague answer, sorry for being so picky :smile: but I've added a new 'mirrored' image where the outcomes are totally different, the orange pair is moving further horizontally ahead while the green ones are almost stationary in the same spot, that IS a big difference, so all in all the outcomes aren't the same at all, is this correct?

    attachment.php?attachmentid=67333&stc=1&d=1394129813.png
     

    Attached Files:

    Last edited: Mar 6, 2014
  10. Mar 6, 2014 #9

    Dale

    Staff: Mentor

    What physics did you use to determine that there is a big difference? What equation did you solve to determine the different outcomes?

    Sure you can draw a picture, but that shows your artistic ability, not the way nature works.

    Is the collision elastic (they bounce off each other undamaged) or plastic (they stick together)?
     
  11. Mar 6, 2014 #10
    Doesn't really matter; if you set two cases to the most extreme angles 180° (AA) with velocities (-1,0) and (-1,0); and 90° (BB) with velocities (0,-1) and (0,1); than you would have particles that either never *collide* and fly next to each other horizontally (AA), versus those that collide 100% head on (BB).
     
    Last edited: Mar 6, 2014
  12. Mar 7, 2014 #11
    Ok, Ignore my previous comment, my friend has given his equations and method that I'll quote below, but first I'll explain the whole concept and why this question in the first place.

    --

    The goal is to simulate a gas made up of slippery frictionless ellipsoids that can slide over each other during interaction. Sort of like these billiard ball-like soap bubbles:

    http://www.800million.org/collisions/billiard_1.jpg [Broken]

    Because this kind of fictitious particle, with the sliding interaction, is nearly impossible to figure out with actual physics equations, the idea was to use 2 programs:
    1. Collision editor: where it's possible to preset the outcome of different kinds of collisions intuitively by hand.
    2. Simulator: that uses the presets from the Collision editor as out come for each collision, to generate this gas.

    So when 2 particles collide in the Simulator the outcome is what is defined in the 'Collision editor'.

    I'm adding a couple of images of:

    1. Collision editor:

    http://www.800million.org/collisions/collision_editor.png [Broken]

    --

    2. Simulator:

    http://www.800million.org/collisions/simulator.JPG [Broken]


    --

    And here is a scheme of what kinds of presets there should be, for a set particle 'A' and an in-flying particle 'B' that changes position relative to 'A', and where things could be mirrored. The 'in between' results should be calculated by interpolation.

    http://www.800million.org/collisions/CE_1.png [Broken]

    -------------


    Now here's the suggested method to solve this:

    --

    That's it. Looking forward hear your opinion. btw any suggestions to tackle this problem are welcome.
     
    Last edited by a moderator: May 6, 2017
  13. Mar 7, 2014 #12
    Sim in 2D, right?
    The whole reason using ovals would seem to be to look at the spins and effect of moments because of the different ways contact between ovals can impact each other at different points around the circumferences, hence causing different moments and spins. But I'm not seeing that your ovals are spinning? ...they will be after collision, so your phi angle tilts are going to be changing..
    Once they are spinning you'll need to know where on the ovals collision contacts occur so that impact calculations can include a component of their moments of inertia as well as their approach speeds of centers of mass.

    I think this means that as the centers of mass of individual ovals approach each other you'll need to know their phi angles at the instant of contact, which sounds like it means each oval is going to have an oscillating boundary with respect to its direction of travel, and when two ovals' centers of mass approach close to the length of the long axis of the ovals (half of each of the two) where contact may be immanent, the phi angles would need to be "projected forward" to both predict a contact time (step) and contact orientation of the ovals, and specific location of contact on each oval circumference to compute relative moments, etc... sounds pretty complicated, but think you need this to assign the impact of collision, its distance and direction from the centers of mass and the resulting effects on the ovals' spins, as well as the directions and speeds of their centers of mass.

    This might be a routine that detects an immanent collision (or keeps track of all the ovals' rotation conditions for each step) and uses a sub to step "ahead" in time to determine what the relative orientations and contact points will be, then sending those values to the main engine for the contact step to calculate moments at contact, resulting phi angles and angular rotation speed after contact, and resulting directions and speeds of the centers of mass after contact.
     
  14. Mar 7, 2014 #13
    Yes.

    3D perhaps one day, first 2D ...


    No, 'spin' shouldn't be included. The reason for this, is when you add 'spin' to the outcome of the collision, than the orientation of the ovals could be anything based on their outgoing velocity, and the time of when their next collision takes place ... also more slippery is more spin(?), or less spin(?) ... so it would probably be fairly meaningless to start presetting the outcome of collisions with 'spin', cause the gas would be chaotic (no control). Thus the orientations should be locked in set directions when the particles leave the collision, based on how they collide. One of the main points also is to get a grip on the number of unique ingoing (preset) collisions to get a fair level of smoothness.

    The actual reason of this concept is to look for possible packing formations sort of like what you can see in the images below, but they are generated thanks to the bulk-volume-interaction of rods (oval particles). So by using a more exotic type of particle/interaction some results might be created with far less particles.

    http://www.800million.org/collisions/GRNLR_1.jpg [Broken]


    ... I guess this first response, exclusion of spin, effects the rest of your comment here:


     
    Last edited by a moderator: May 6, 2017
  15. Mar 7, 2014 #14
    That's because the properties are vague. If your ovals won't spin and energy is conserved than their shape doesn't really matter at all (as far as the outcome of the collision) and all the collisions in the first post will indeed produce identical outcomes. Either way, I strongly recommend that you program you collision generator in the center of mass reference frame.
     
  16. Mar 7, 2014 #15
    What is vague about the properties? It are particles with spin=0 that collide, coming from different directions. I agree that the outcome will be unnatural, because it will be manipulated by the program, but that's irrelevant regarding my question.

    What my question is about is if in a natural setting the outcome would be different for AA, BB, CC and DD? ... and yes spin, change of momentum and energy loss may all be considered during the collision. This is important to know because if the outcome would be for each case the same, than only one 'preset' can be used for a lot of collisions; otherwise there need to more presets for each of those unique cases.

    The shape is important, because it will be the heart of each collision, and serving like an oval roundabout redirecting particles into a specific direction, depending on how they are orientated towards each other and how they make contact. Therefor it should be a perfectly normal and natural until the point that they start exiting the collision which is in fact something else.
     
  17. Mar 8, 2014 #16

    Dale

    Staff: Mentor

    Intuitively is fine, but then you are just doing some computer programming or a video game. You are not doing physics. If you want to do physics then you need to actually solve for this physically, not intuitively. If you just want to do a video game then there is nothing to discuss here in Classical Physics.

    Your idea for presetting outcomes is a good idea. That way you can solve the equations in advance and plug in the results as needed. It trades memory for computation speed. As has been suggested earlier, your outcomes table should be written in the center of momentum frame. That will reduce the number of entries by a lot. The process would be:

    Transform to center of momentum frame
    Lookup collision results
    Update velocities
    Transform back to original frame
     
  18. Mar 8, 2014 #17

    Dale

    Staff: Mentor

    If you do not include spin then either
    a) The collisions must be the same as a collision of a spherical object (i.e. the forces must be exerted along the line joining the centers of mass, regardless of the point of contact)
    b) You will violate the conservation of angular momentum

    You cannot both conserve angular momentum and have forces which do not pass through the center of mass.
     
  19. Mar 8, 2014 #18
    Until a certain point it is Classical Physics and that's the part I'm questioning here.

    So what I now have found out regarding that is:

    The relative velocities that they are moving towards each other is different for each case (colored vertical arrows), although the velocity and time that they move towards the rendezvous point is for each case the same (black arrows); and because of this difference in velocity the normal reaction force is different so the torque is different for each case.

    A second point was that if you would look only at these relative velocities, one wouldn't know that there's a possible difference in angle of approach, and for this someone told me:

    To calculate the collisional impulse all you need is
    * the orientation of the objects relative to the tangent line
    * the relative velocities of the points on the body that are going to make contact (it doesn't matter what combination of linear and angular velocity causes this).
    That is, the key variable is the velocities of the contact points, not of the centers of mass.
     
  20. Mar 8, 2014 #19

    Dale

    Staff: Mentor

    Not if the spin is to remain 0. You cannot have it both ways.
     
  21. Mar 8, 2014 #20
    Why not? I mentioned ...

    So I guessed one can figure out what different types of collisions there are in Classical Physics by using the 'not centers of mass method', and than manipulate those results and create presets, this part has of course no longer anything to do with Classical Physics. Why would it be impossible to make the jump between the two in a Collision_editing program?
     
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