Do you have a reference for how to extend Newtonian mechanics to collisions or passing-through of point particles subject to gravity? how about people complaining about 3 body collisions?
Bringing in energy and momentum doesn’t sound helpful to me because they are both infinite at the point of collision.
My understanding is that both of the choices has a unique analytic extension to the complex plane away from the point of collision. Most limiting approaches will agree with this one. In particular, Richard Kennaway’s approach (to non-collision) is perturb the particles into another dimension, so that the particles don’t collide. The limit of small perturbation is the passing-through model.
For elastic collisions, I would take the limit of small radius collisions. I think this is fine for two body collisions. In dimension one, I can see a couple ways to do three body collisions, including this one. The other, once you can do two body collisions, is to perturb one of bodies, to get a bunch of two body collisions; in the limit of small perturbation, you get a three body collision. But if you extend this to higher dimension, it results in the third body passing through the collision (which is a bad sign for my claim that most limiting approaches agree). When I started writing, I thought the small radius approach had the same problem, but I’m not sure anymore.
Jung vs jr fhccbfr gung gur obqvrf pna cnff guebhtu rnpu bgure? Ubj qbrf gur flfgrz orunir nf gvzr cebterffrf?
Vg’f rnfl rabhtu gb rkgraq arjgbavna zrpunavpf gb unaqyr gjb-cnegvpyr pbyyvfvbaf. Whfg cvpx bar bs “rynfgvp pbyyvfvba” be “cnff guebhtu rnpu bgure”, naq nccyl gur pbafreingvba ynjf naq flzzrgevrf. Ohg V’z abg njner bs nal cebcbfnyf gb unaqyr guerr-be-zber-cnegvpyr pbyyvfvbaf: va gung pnfr, pbafreingvba bs raretl naq zbzraghz vfa’g rabhtu gb qrgrezvar gur bhgchg fgngr, lbh’q arrq fbzr npghny qlanzvpf gung ner qrsvarq ba gur vafgnag bs pbyyvfvba.
Do you have a reference for how to extend Newtonian mechanics to collisions or passing-through of point particles subject to gravity? how about people complaining about 3 body collisions?
Bringing in energy and momentum doesn’t sound helpful to me because they are both infinite at the point of collision.
My understanding is that both of the choices has a unique analytic extension to the complex plane away from the point of collision. Most limiting approaches will agree with this one. In particular, Richard Kennaway’s approach (to non-collision) is perturb the particles into another dimension, so that the particles don’t collide. The limit of small perturbation is the passing-through model.
For elastic collisions, I would take the limit of small radius collisions. I think this is fine for two body collisions. In dimension one, I can see a couple ways to do three body collisions, including this one. The other, once you can do two body collisions, is to perturb one of bodies, to get a bunch of two body collisions; in the limit of small perturbation, you get a three body collision. But if you extend this to higher dimension, it results in the third body passing through the collision (which is a bad sign for my claim that most limiting approaches agree). When I started writing, I thought the small radius approach had the same problem, but I’m not sure anymore.