How do you decide on the sign of a Hamiltonian function?
For example, I have the following system of differential equations:
x'=y
y'=-\dfrac{3}{2}x^{2}-2x
With the following Hamiltonian:
H^{\oplus}=\dfrac{1}{2}x^{3}+x^{2}+\dfrac{1}{2}y^{2}
because \dfrac{dH^{\oplus}}{dt}=0. But if...
It's the same, but I made a calculation error. I did \sqrt{25+4}-3 instead of \sqrt{25+4}-2
I prefer my version though, since it's in the form of c times a time.
In my formula it's also much more obvious that d increases with increasing a'.
x\left(t=0\right)=c^2/a'
So I should define a new axis x'' then?
x''=x-c^2/a'=c\sqrt{c^2/a'^2+t^2}-c^2/a'=c\left(\sqrt{c^2/a'^2+t^2}-c/a'\right)
If a' goes to infinity:
x''=ct
If a' goes to zero:
x''=c\left(\sqrt{c^2/a'^2}-c/a'\right)=0
Let's say a'=0.5c/yr, t=5 yr...
The path described by a constantly accelerating particle is given by:
x=c\sqrt{c^2/a'^2+t^2}
where a prime denotes an observer traveling with the particle and a letter without a prime a resting observer.
If we leave the c^2/a'^2 out it reduces to x=ct, which makes sense. The distance...
The higher bandwidth and smaller antenna make sense and is something I already should've known.
Of course higher frequencies are damped more easily. I was thinking that orange light essentially is Wi-Fi at a 200k times larger frequency.
That link was not really helpful. It details how you should write entries in a list of references for which I use Bibtex and it explains how you should use parenthetical references (which I don't, I use [#ID], which is regularly seen in the natural sciences). It doesn't explain where citations...
I'm not sure where to put this question, so I'll try it here. I'm currently writing a report and I'm asking for advice on citations. I know that when you write down a fact or an idea which is not original, you add a citation which explains where you got it from (e.g. bananas are yellow [1])...
I'm trying to make a MATLAB plot with two types of data, i.e. temperature and air flow rate. Since the temperature and air flow rate are on different scales I wanted two y-scales and since there are quite some data sets, I wanted to make the two air flow rates bold.
I tried this, but it doesn't...