Timeline for Non-uniqueness of solutions in Newtonian mechanics
Current License: CC BY-SA 3.0
10 events
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| Feb 2, 2023 at 18:47 | comment | added | mr_e_man | But that's assuming that there are actually two collisions happening in succession. If it's considered as a single collision, then the direction of the force on the ball is not determined; it could be anywhere between the two walls' normal vectors. | |
| Feb 2, 2023 at 18:39 | comment | added | mr_e_man | Another example is a ball colliding with two walls at once (i.e. an inside corner), where the angle $\theta$ between the walls is something other than $90^\circ$. Mathematically, two reflections in planes make a rotation by twice the angle between the planes, but the direction of rotation depends on the order of the two reflections. So the ball's velocity can turn by $2\theta$ either left or right. | |
| Oct 20, 2013 at 2:06 | comment | added | user31350 | Thanks, Nanite. I think this is along the lines of what Lanczos was getting at. Would you happen to know of any treatment of this problem (3 spheres scattering elastically)? I googled it and didn't find anything, and I've tried to work it myself and the math is getting pretty ugly. | |
| Oct 19, 2013 at 21:00 | comment | added | Nanite | There are a variety of hard-contact problems in Newtonian mechanics which fail to give unique solutions. For example, the simultaneous collision of three spheres. Of course such problems are obviously a mathematical curiosity since they involve infinitely sharp contact potentials, but they are fun to think about. There are also some strange solutions that occur with certain initial conditions (such as a swinging pendulum given just enough energy to reach its apex), also of course unrealistic since the initial conditions have to be perfectly fine tuned. | |
| Oct 19, 2013 at 20:49 | answer | added | Orcun | timeline score: 1 | |
| Oct 19, 2013 at 19:52 | review | First posts | |||
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| Oct 19, 2013 at 19:43 | answer | added | user4552 | timeline score: 2 | |
| Oct 19, 2013 at 19:43 | comment | added | Qmechanic♦ | For non-determinism in Newtonian mechanics, see e.g. Norton's dome | |
| Oct 19, 2013 at 19:43 | history | edited | Řídící | CC BY-SA 3.0 |
added 46 characters in body
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| Oct 19, 2013 at 19:37 | history | asked | user31350 | CC BY-SA 3.0 |