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!
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...
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
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
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 $L$
@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
@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
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...
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!
I'm sorry for being asking non clarified questions. That won't be repeated. Is it ok to remove the ban?
