Are you saying that practically speaking we can't know F(t) or T(t)?
Can you elaborate on the relativistic implications?
I am very determined to fully understand this concept. Thank you kindly.
Hi all,
I am reading a book on spacecraft engineering in the section about trajectory dynamics. They define linear and angular momentum as:
##I = \int_{0}^{\tau}{F}dt## (Linear Momentum)
##L = \int_{0}^{\tau}{T}dt## (Angular Momentum)
But they (and so many other sources) always mention the...
Sorry I'm not familiar with your method. I don't understand why you substitute "t+δt" for t. What approach are you using here? Could you elaborate or direct me to some further reading?
Cheers :)
When sketching a root locus of a simple closed loop negative feedback system (with positive gain K).... if you have more poles than zeros, we know that they will tend towards infinity along some asymptotes. How do you know which pole will travel along which asymptote?
For example in the...
Hi,
I want to verify that the form of a particular solution satisfies the following ODE:
v' + (b/m)v = u/m
with
vpart= ∫e-(b/m)(t-r) (u(r)/m) dr
where the limits are from 0 to t
So I tried to differentiate v with respect to t, in order to substitute it back into the equation. But, how do...
Conceptually, what does it actually mean to take the 'moments about a point' on a body, even if that point is not the center of rotation of the body (center of mass say). For example, we could take the moments about a point not even 'in' the body, so what does this value represent?
I am...
So I have the following shape for which I want to calculate the inertia matrix. Basically I just want to know what limits of integration I should use if I am using spherical coordinates. Assume the convention that phi is the angle from x to y in the xy plane and theta is from z to the xy plane...
Homework Statement
So, I have found a general solution to a system of linear first order ODE's and this is what I got:
X = c1v1e^(-1+2i)t + c2v2e^(-1-2i)t
where v1 = [-1+2i, 5], v2=[-1-2i,5]. The question is, how do I now change this solution into its real equivalent? i.e. I dont want any...
Homework Statement
A liter of air, initially at room temperature and atmospheric pressure, is heated at constant pressure until it doubles in volume. Calculate the increase in its entropy during this process.
Is there a way to calculate this using the thermodynamic identity (ie. without the...
Could someone please elaborate on this and show exactly how we come up with the coefficients being the relative probabilities..? Just keep it 1dimensional.Thank you!
Ok, but how physically does this make sense? How does the fact it goes past a potential change its path? I suppose I still don't fully understand what potential wells represent physically.
What do you mean when you say transmitted/reflected? If we are talking about a beam of electrons moving towards an attractive square potential (-ve well), what is meant by whether it is transmitted or not..? (In 1D)
"Scattering" by a potential
When we have an unbound particle travelling past a potential well, what does it mean when it is said that the potential well will "scatter" the particle?
Thanks for the detailed response Mike. I can see how just statistically working it out, it shows that bosons are more likely to be together... However, I came across this article which describes a sort of 'avalanche' process:
http://eve.physics.ox.ac.uk/Personal/ruprecht/BEC/pw2/pw2.html...
So I think I have the basic idea of what phase-space is... basically a way of representing all possible states of a system in some n dimensional space. So, what then, is phase-space density?
If we take most of the energy out of the system so theres practically no energy, then there may be a few bosons in higher energy states but most of them will be in the lowest possible state, that is what I got from it.
Are you saying there is some other reason why they go to the ground state?
Oh, so the fact that we have lowered them to around ground state means most of them will, statistically, be in the ground state. So this tendency is purely a statistical one?
Oh so its just like the basic statistical physics explanation... am I right to say however, that they all want to occupy the GROUND state? rather than just be together in any state?
I am doing some research on Bose-Einstein condensates and was hoping someone could give me a non-mathematical reason as to why bosons 'want' to occupy the same ground state. I think its details come from Bose-statistics, but is there a simplified way of explaining it? Thanks
I had a feeling that was the answer. Ok, well, how do we know that the expansion coefficients are the relative probabilities? is it because we observe this?
Can someone please explain why the representation of a wavefunction as an expansion of basis eigenfunctions actually gives us something of physical meaning? For example, it can tell us the probabilities of measuring a particular eigenvalue (depending on the expansion coefficients).... I mean its...
I am not sure whether there is any difference between differentiating complex and real numbers... I am just trying to differentiate:
e^(2+3i)x = (2+3i)e^(2+3i)x
Is this correct? I have a feeling its not this simple.
Hi Shyan, thanks so much.
Now I have another question, if we have a potential well diagram as I showed above and there is a particle with more energy than the top of the well, why is it that we know for sure it wont go into that well. I mean, as you said there are forces causing this potential...