 12:39 AM
@NikeDattani I know the formalism but have not heard of specific packages for it.

10 hours later… 10:38 AM
If the constraint equation is expressed with inequality ( like < or <=), is it considered non-holonomic?
like for particles in closed spherical shell?

2 hours later… 12:58 PM
Yes, that's a classic example of a non-holonomic constraint iirc

2 hours later… 2:35 PM
0  I have a question about my Physics Stack Exchange post: ODE of a beam on an elastic foundation Please reopen my edited question. This was not a homework-type question! I have presented a solution from a book, which I do not understand. Thank you! 3:32 PM
I don't really get the point of the "candidate score" thing for elections. Seems like it's trying to be a tl;dr

1 hour later… 4:42 PM
0  I asked this question about what it is (if anything) that provides and upper limit to the speed of a turbine in a fluid stream: Maximum rotation rate of a turbine in a fluid with a given speed It was closed as "engineering". The linked meta post says: Are any engineering questions allowed? Quest... I think rigid bodies allow for time asymmetric potentials :/ Is this a known fact? 5:05 PM
No reason why you can't just throw a delta potential in to a non-relativistic Lagrangian I don't think
@MoreAnonymous Skimming your post it looks like you set a constant $\alpha$ equal to a function, but ignored differentiating $\alpha$ in the EL equations $\alpha$ is a constant 0  I'm sorry for being asking non clarified questions. That won't be repeated. Is it ok to remove the ban? The last equality in your post doesn't look like a constant, and if it is just the value of that function at a point then it's not the equations you were trying to get in the first place 5:19 PM
@bolbteppa The classic slap
Interaction that lasts only a moment in time 5:38 PM
Right that's a delta function centered at $t_{unfortunate}$ 5:56 PM
@bolbteppa If you solve it you get the collision you wanted. I agree this is not a time symmetric potential though
Note if you go backward in time $\alpha \neq \frac{m_1 m_2}{m_1 + m_2} \frac{(\vec r_1 - \vec r_2) \cdot (\vec v_1 ' - \vec v_2 ') }{|\vec r_1 - \vec r_2|^2}$
the post collision velocities are $\vec v_1'$ and $\vec v_2'$ 6:19 PM
You derived $m \ddot{x}_1 = - 2 \alpha(x_1 - x_2)\delta(t - t_c)$. This is not $\frac{d \vec p_1}{dt} = - \frac{2 m_1 m_2}{m_1 + m_2}\frac{(\vec r_1 - \vec r_2) \cdot(\vec v_1 - \vec v_2)}{|\vec r_1 - \vec r_2|^2} (\vec r_1 - \vec r_2)\delta(t-t_c)$ and you can't just set $\alpha$ to be equal to the missing part $\alpha = \frac{m_1 m_2}{m_1 + m_2} \frac{(\vec r_1 - \vec r_2) \cdot (\vec v_1 - \vec v_2) }{|\vec r_1 - \vec r_2|^2}$ because its a function but you treated it like a constant in $L$ 6:42 PM
@bolbteppa So I think of things physically .. .Is there any experiment you can do distinguish between both cases? Let $\tilde \alpha = \frac{2 m_1 m_2}{m_1 + m_2}\frac{(\vec r_1 - \vec r_2) \cdot(\vec v_1 - \vec v_2)}{|\vec r_1 - \vec r_2|^2}(t)$ and $\alpha = \tilde \alpha(t_c)$ ? Technically $\delta(t - t_c)$ is zero everywhere except at $t_c$ where it's infinite so not sure what it means physically, usually there's an integral somewhere letting us avoid these issues but here I don't see how you can invoke one. Further I'm not sure what you're saying but it sounds like what you're saying could mean we can replace $\alpha$ by anything not just one specific form 7:08 PM
@bolbteppa I think the force experienced in an ideal collision is infinite (this is well known) ...$\Delta p / \Delta t$ ... Change in momentum is finite while delta t goes to $0$ ... And yes you could write any $\alpha$ but then you wouldn't be modelling a collision

3 hours later… 9:47 PM
0  I read in an answer to a question I read that a defense for if a question is accused of being non mainstream is applications of established science to new systems where they clearly apply. One naive interpretation I can think of is that if it's possible to use the mathematics of a model in mainst... 10:37 PM
@MoreAnonymous collisions are when the particles touch, not a fixed time regardless of particle position
as someone said in the comments, you probably want to look at this en.wikipedia.org/wiki/Hard_spheres