What is the relationship between lambda and stability in astronomical systems?

  • Thread starter Thread starter check
  • Start date Start date
check
Messages
144
Reaction score
0
Hi everyone,
I've got this assignment for astronomy class to do:
http://img145.imageshack.us/img145/7500/projoutlinevk1.jpg

Basically I'm having a bit of trouble for the part in the image that I highlighted. I can't seem to figure out \lambda. I know what the behavior of the system is supposed to look like for different cases of \lambda, I just can't seem to come up with it. Any help would be great!
 
Last edited by a moderator:
Physics news on Phys.org
Anyone good with stability analysis?
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

What Values of ##\lambda## Allow Non-Trivial Solutions in This Linear System?
Replies
3
Views
1K
Dependent Motion: Sample Problems & References
Replies
1
Views
3K
Dynamic Damping in a simple spring system
Replies
6
Views
2K
How can I use Gauss elimination to zero out the elements of a block system?
Replies
4
Views
2K
Double (Iterated) Integration. Where am I going wrong?
Replies
2
Views
2K
How Do Eigenvalues Determine Stability in Non-Linear Dynamics?
Replies
6
Views
2K
What is the relationship between stability and the derivative of a fixed point?
Replies
10
Views
5K
I Relationship between frequency and power for sound?
Replies
11
Views
5K
What are the job prospects for Astronomers in the next 10-15 years?
Replies
2
Views
3K
A QFT and transitions between momentum states
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top