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Dec
8
comment What Is the Physics principle behind dropping a stone into a cup of water?
I wasn't the one who downvoted, but I can understand that, since the second sentence is clumsy and requires a bit of thinking on what was meant.
Dec
3
comment How does a bowl of hot water move by itself?
I do observe this phenomenon from time to time with plates and hot food on it. For me usually the plate also rotates in addition to mere displacement. The displacement is of no more then 2-3cm I recon and the rotation of the edge is of the same magnitude. The whole movement takes around the second, then the plate stands still. When I pick up the plate there is a sizeable amount of steam condensate on the underside of the plate and on the surface of the table.
Sep
30
awarded  Explainer
Sep
27
awarded  Popular Question
Jul
16
awarded  Nice Answer
Jul
2
awarded  Curious
Jun
15
revised Formalism to deal with discontinuous potentials in classical mechanics (hard wall, hard spheres)
added 886 characters in body
Jun
14
awarded  Yearling
Jun
11
comment How close does light have to be, to orbit a perfect sphere the size and mass of Earth?
I agree with Chris White --- it would be nice to mention why light is being out of scope Newton's gravity theory, that is to specify the limitations of classical theory and when in general we do need to resort to GRT.
Jun
9
revised Formalism to deal with discontinuous potentials in classical mechanics (hard wall, hard spheres)
minor formatting
Jun
9
accepted Formalism to deal with discontinuous potentials in classical mechanics (hard wall, hard spheres)
Jun
9
comment Formalism to deal with discontinuous potentials in classical mechanics (hard wall, hard spheres)
If you require only $U_\text{max}$ being greater or equal than the initial kinetic energy, then $0=\frac{m}{2} \nu^2(0_+) + [U_\text{max} − \frac{m}{2} \nu^2(0_+)]$ may not have solutions at all with $\nu(0_+) \in \mathbb R$. It will have a solution $\nu(0_+) = 0$ only if $U_\text{max}$ equals to a kinetic energy of an incident particle, but that makes it dependent on the particle momentum.
Jun
9
comment Formalism to deal with discontinuous potentials in classical mechanics (hard wall, hard spheres)
@auxsvr the problem is I do not see how they really solve the problem --- whenever I try to rigorously conduct the derivation I got stuck. And it seems to me that others hold the same opinion. I have commented on your answer on certain things I do not understand. Once again what is being sought --- Hamiltonian equations which can be solved as is, without resorting to any supplementary physical arguments. You see, Hamiltonian equations should be self contained, fully describing the system evolution, right?
Jun
9
comment Formalism to deal with discontinuous potentials in classical mechanics (hard wall, hard spheres)
Oh, I got it, but still it would be nicer to be written. Moving along the derivation, as far as I understand you show that momentum when $x > 0$ is $0$ but it does not justify that is should reverse. Andy why is the energy is $1$ as you said? It should be $p^2/(2m)$ in any case. Moreover, with the potential fixed being equal $1$ does not prohibit the particle to enter the region if its kinetic energy is greater then $1$.
Jun
9
comment Formalism to deal with discontinuous potentials in classical mechanics (hard wall, hard spheres)
Could you please elaborate on how you have integrated $\int_{0_-}^{0^+} \dot \nu \, dx$ ? This is not so obvious.
Jun
8
answered Formalism to deal with discontinuous potentials in classical mechanics (hard wall, hard spheres)
Apr
5
awarded  Benefactor
Apr
2
comment Formalism to deal with discontinuous potentials in classical mechanics (hard wall, hard spheres)
oops, I have awfully miscalculated the time. If somebody cares, the correct reasoning should be following: The distance traveled is $\varepsilon E_0 = v_0 (\tau / 2) - 1/2 \, \varepsilon (\tau/2)^2 $. If we divide this expression by $\varepsilon$, will get the answer in the form $\tau = \varepsilon f(E,v_0)$ which is linear in $\varepsilon$.
Apr
1
comment Hamiltonian function for classical hard-sphere elastic collision
Milton, have a look at my related question physics.stackexchange.com/questions/105318 As for you derivation, I bet your calculation of $\Delta P_1$ is wrong, you should conduct the integration more accurately with greater level of details.
Mar
31
comment Formalism to deal with discontinuous potentials in classical mechanics (hard wall, hard spheres)
If noone comes with an elegant framework which would avoid potential regularisation in the remaining bounty time, I will accept Qmechanic's answer.