Recent content by rakso

True. However, doesn't the problem become spherical?

I like this suggestion! I suppose it's not water that flows though, but perhaps the fluid has the same properties?

Hi! Water is flowing in a converging duct, with the angle α, see the figure. My task is to find a real-life phenomenon / application of this model, and later solve it numerically / analytically where this fluidproblem occurs. However, my imagination is kinda slow today, what are some fun /...

I see, this is the wrong part. So I confused Diracs frame while traveling and Diracs frame on Alpha?

I don't get this though. Dirac has a watch on him and takes a long nap and waking up when he arrives at Alpha. He looks at earth, in rest frame of Alpha, and measures Earth to be 4.37 LY away. He then looks at his watch and sees it took 5 years. He must then draw the conclusion that he traveled...

When Dirac arrives at Alfa Centuri and looks back at earth, the distance should be 4.37 LY. How can the speed be symmetrical if the time it took differs but the distance dont? I mean when Dirac steps out on a planet, let's say it's not moving relative to earth, the distance should be the same...

Alright, what speed is the Earth traveling away from Diracs spaceship?

Hi, I'm taking an introduction course to Special Relativity and encountered a fairly simple problem: Dirac travels to alfa centauri, which is 4.37 lightyears away. He stays there one Earth year and then travels back, and when he comes back he has aged 5 years. At what speed did he travel...

Found a solution here! https://math.stackexchange.com/questions/2443225/pole-placement-control-theory

Summary:: Control Theory root equation pole Hi, I ran into a simple question but somehow I can't get it right. My work this far: ## G_0(s) = G(s) \cdot K \cdot \frac{1}{T_I s} = \frac{k}{\tau s +1} \cdot \frac{2\beta \tau -1}{k} \cdot \frac{2\beta^2 \tau}{Kks} = \frac{2\beta^2\tau}{s(\tau s...

Ah, I see. So for example, if we're in ## R^3 ##, ## \vec{F} ## would then be ## \vec{F} = (p_1 \partial_1 + p_2 \partial_2 + p_3 \partial_3) \vec{E} = (p_1 \partial_1 E_1 + p_2 \partial_2 E_1 + p_3 \partial_3 E_1)\hat{e}_1 + (p_1 \partial_1 E_2 + p_2 \partial_2 E_2 + p_3 \partial_3...

Hi! The topic is electrodynamic but it's a question about Nabla identity. Given $$ F = (p \cdot \nabla)E $$ How does one compute F? Is this correct? $$ F = \sum_{i} p_i \partial_{i} E_{i} e_{i} $$

Hi, Given a mechanic-problem, I've linearised a system of two differential equations, which the origin was Lagrange-equations. The system looks like this; $$ 5r \ddot{\theta} + r \ddot{\phi} + 4g \theta = 0´ \\ 3r \ddot{\theta} + 2r \ddot{\phi} + 3g \phi = 0 $$ $$ $$ And I shall find the...

m = Particles mass, Omega = Systems angular frequency, v' = particles velocity. Attempt at a Solution: $$ F_{C} = -2m \bar{\omega} \times \bar{v}^{'} = -2 \bar{\omega} \times \bar{p} = 2 \bar{p} \times \bar{\omega} $$ Let $$ \bar{\omega} = \frac {\bar{r} \times \bar{v}} {r^2}, \alpha = \frac...

I think I got it, defining ##0## can sometimes be tricky. Thanks for great answers, MB!