Recent content by RiotRick

Ok I've found the solution on the caltech website. It's public and open, so I guess I can link it here: http://www.feynmanlectures.caltech.edu/II_40.html it's 40-4. But how can I obtain the Formula ##h`=\omega^2*r^2/2g##

Fig1: Fig2: We haven't covered this topic yet, but they expect us to solve it and I'm not 100% sure what I'm doing. a) ##C_r =\oint{\vec{v}*\vec{dl}} = \int{\omega*r*dl} = \omega*\int{r*r*d\phi} = \omega*r^2*2pi## b) Now here I begin to struggle. If v is constant, can I simply pull it out of...

But isn't that exactly what I tried with:

okay I see. I got this wrong about the Matrix. ##lim_{h \rightarrow 0} \frac{||f(x_0+h)-f(x_0)-A(x-x_0)||}{||h||}=0## where A is my mxn matrix of the linear mapping of the partial derivatives. So A = (1,1) in my example

In my notes and in wikipedia: A function with more than 1 variable is differentiable if:

I'm now quite buffled that my approach with the definition is "hard to follow". First I need to show that the function is differentiable and then calculate Df. I use only the definition of differentiability. With the first steps I calculate my Jacobian Matrix to use it for the J(h). I don't know...

Homework Statement Examine if the function is differentiable in (0,0)##\in \mathbb{R}^2##? If yes, calculate the differential Df(0,0). ##f(x,y) = x + y## if x > 0 and ##f(x,y) =x+e^{-x^2}*y## if ##x \leq 0 ## (it's one function) Homework Equations ##lim_{h \rightarrow 0}...

Homework Statement Homework Equations euler ##e^{ix} = cos(x) + i*sin(x)## ##e^{-ix} = cos(x) - i*sin(x)## The Attempt at a Solution I'm starting with differential equations and I'm trying to understand this solution including complex numbers: First we determine the zeros. I understand that...

Homework Statement Let ##f:X\rightarrow Y## with X = Y = ##\mathbb{R}^2## an euclidean topology. ## f(x_1,x_2) =( x^2_1+x_2*sin(x_1),x^3_2-sin(e^{x_1+x_2} ) )## Is f continuous? Homework Equations f is continuous if for every open set U in Y, its pre-image ##f^{-1}(U)## is open in X. or if...

Is my estimation for ##\Delta v## plausible? It already reaches the higher ##r_b## but can't stay on it and get pulled back to the lower ##r_A##. So to stay on the higher orbit in a circular orbit ##\Delta v## is around ## \sqrt(2*G*\frac{M}{r_B}) - \sqrt(2*G*\frac{M}{r_a})## from...

But at least the amount of fuel does depend on the mass or ist that also wrong?

Homework Statement Consider an elliptical orbit of a satellite (of mass m) around the Earth (of mass M >> m). The perigee is at ##r_A## and the apogee at ##r_B##, as measured from the centre of the Earth, itself located at one of the focal points of the ellipse (see Fig. 1). We work in an...

Homework Statement Let X = ##\mathbb{R^m}## and ||.|| be a Norm on X. The dual norm is defined as ##||y||_*:=sup({\langle\,x,y\rangle :||x|| \leq 1})## a) Show that ##||.||_*## is also a norm b) Construct two norms ##||.||^O## and ##||.||^C## so that: {##x:||x||^O=1##} is a regular octahedron...

I should have posted all the questions: a) Is there a circular orbit for which an object would hover continuously above the same point on Earth? What is the radius rGSO of that geostationary orbit? Hint: for a circular trajectory, the centrifugal force experienced by the object balances the...

Homework Statement In the far future, humans have built a space elevator as a cheap means of access to space. However before that could be done, a few basic principles had to be worked out. . . a) What is the minimum initial speed (in an Earth-centered inertial reference frame) needed for an...