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...
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...
"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?
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?
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
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.
So I have looked up some related posts about potential wells but none of them really actually talk about what a potential well IS... what does the line on the graph actually tell us? what potential is it talking about?
How would you prove that if the curvature of a 'curve' in R3 is zero that the line is straight? All I have learnt about is the Serret Frenet equations which I thought only apply when the curvature is non-zero? How do you define normals/binormals in this case?
I'm not sure if this is enough...
I was wondering whether anyone has experience in astronomy simulations. If so, what language do you use and recommend? I've done Haskell and a very small bit of C++... I've been told Python is good, what are your thoughts?
Also are there any good websites that may get me started?
Thanks
We are currently learning about solenoids in my physics class, and am very confused about where this potential drop comes from across a solenoid. I understand that an opposing electric field is created when a switch is first opened because of Faradays Law and the fact that the magnetic flux...
Homework Statement
Let k be a natural number, and r a real number with |r|<1. Prove (by induction on k) that for any polynomial P of degree k, there is a polynomial Q of degree k with Q(n+1)r^(n+1) - Q(n)r^n = P(n)r^n
Hint: consider differences of successive terms for (n^k)(r^n) and use the...
I have a problem where it requires me to find when a laser should be fired at an asteroid to ensure that in the reference frame of the asteroid, the laser hits the back and front within 1 millisecond. I thought that I could define events in S' such that the front and back are hit at t' = 0, and...
Homework Statement
A truck is to be towed using two ropes. If the resultant force is to be 950N, directed along the positive x axis, determine the magnitudes of forces F1 and F2 acting on each rope and the angle at which rope two pulls to ensure that the magnitude of F2 is a minimum. F1 acts...
My textbook describes how some functions are not well approximated by tangent planes at a particular point. For example
f(x)= xy / (x^2 + y^2) for x /= 0
0 for x = 0
at (0,0) the partial derivatives exist and are zero but they are not continuous at...
Homework Statement
Integral[ x - 2|x|]dx from [-1,2]
The Attempt at a Solution
Wouldn't it become x^2/2 - 2x^2/2 so x^2/2 - x^2 and then -x^2/2?
So from [-1,2] it would just be
-((2^2)/2) - - ((-1)^2/2) which is -1.5 but the answer is -3.5.....
Homework Statement
Use polar coordinates to find the volume of the given solid:
Under the cone z = Sqrt[x^2 + y^2]
Above the disk x^2 + y^2 <= 4
2. The attempt at a solution
I tried using formatting but I couldnt get it right so I'll explain...I changed variables by making the upper and lower...
I'm doing work on polar coordinates in double integrals. Could someone explain why when circles aren't centered on the origin the angle only varies from (if it is translated above the origin) 0 to pi. I thought the angle was supposed to be the angle in the circle, so if its a full circle then 0...
Homework Statement
So I have to use the type I type II region formula to find the volume under the equation (2x-y) and over the circular domain with center (0,0) and radius 2. Do I have to split this circle into semi-circles and treat it as 2 type I domains? I got the following limits for...
So I have to use the type I type II region formula to find the volume under the equation (2x-y) and over the circular domain with center (0,0) and radius 2. Do I have to split this circle into hemispheres and treat it as 2 type I domains? I got the following limits for the top half, but I get...
Just wondering how this is simplified to the third line:
If w, z are complex numbers
wz = rs( cos\alpha + isin \alpha ) (cos \varphi + isin \varphi)
wz = rs(cos\alpha cos \varphi - sin \alphasin\varphi) + i(sin \alphacos\varphi + cos \alpha sin \varphi))
wz = rs(cos (\alpha...
Homework Statement
A polarized water molecule is near a long charged wire and experiences a force due to the charge. How do you determine the net force on this molecule assuming the molecule is perpendicular to the center of the rod and nothing polarizes further.
The Attempt at a Solution...