(1) For a real function, g(x), the Fourier integral transform is defined by
g(x) = \int_{0}^{\infty} A(\omega )cos(2\pi \omega x)d\omega - \int_{0}^{\infty} B(\omega )sin(2\pi \omega x)d\omega
where
A(\omega ) = 2 \int_{-\infty}^{\infty} g(x)cos(2\pi \omega x)dx
and
B(\omega ) = 2...
I have been working with elliptical motion for a while, so am aware that when one body revolves around another in an elliptical orbit it sweeps out equal areas in equal times (measured from a focus).
However, I am not sure if the same applies to parabolic motion. If, say, a comet approaches...
I am trying to solve an equation:
arccos(Y) = arctan(Y), where Y = 1/x
This turns into a quartic equation:
x4 - x2 - 1 = 0
It looks simple enough to simplify further; however, I must be having a brain-fart because I can't do it. I'd like to avoid resorting to a numerical solution...
Consider the following:
On a circle of radius 1, two points are marked: P1 and P2.
Two lines are drawn from the center of the circle:
one from the center to P1,
the other from the center to P2.
The angle between these two lines is \theta.
One more line is drawn: from P1 directly...
Some time ago I saw a thread in which was mentioned a root-finding algorithm that converges twice as fast as the Newton-Raphson method. Newton-Raphson converges to a zero at a quadratic rate, and a poster pointed out that another algorithm converges to a zero at a quartic rate.
I have tried...
A spinning top has angular momentum that creates a force that keeps it from falling over, and it precesses. Mass in motion has momentum and/or angular momentum.
That made me wonder:
Does fluid in motion create angular momentum?
If so, how would it materialize?
Consider a fictional...
I recently came across a bookmarking site aimed at students:
http://www.brainify.com/" [Broken]
It is not specifically for Math, Physics, and Engineering students, but students in general. To sign up for an account, users need to use a college or university email address.
There are...
I came across an interesting story today and thought I would share it here.
http://www.fastcompany.com/magazine/132/brilliant.html" [Broken]
Neat stuff.
Although I do wonder, even if they get it working and feasible for large-scale adoption, would there be any adverse health affects? (I...
Hi, folks.
I am looking for some help to understand the physics of a water pendulum (in fact, I don’t even know if my terminology is correct). It has been several years since I left school and my math/physics tools are rusty.
Here’s the set up:
Whenever I come back from the beach with a...