I don't know about doing this cold. This occurred to me . But I will be knocked out cold by the time I solve this matrix analytically and then calculate its eigen values :P
There seems to be no respite to the complexity . There has to be a better substitution . Thanks
I don't know what to do .
Where should i have started substitution ?
I am beyond hope right now and i am not able to cross the mental block.
Hints and suggestions are wasted on me right now. You will have to explain to me explicitly if I am to solve this :)
Thanks
I used the transformation suggested. I am stuck at the page 2.
The un-elegance of the jacobian prompts me to believe there could be a better substitution or I am wrong somewhere in the beginning.
Can u suggest a way out ?Page 1 : http://postimg.org/image/81ljfhhdf/
Page 2 ...
Sorry I am a bit confused by what you said . Let me reiterate what you said to confirm that I understood you.
I have the equation
sin (x-y) = -a sin x - a sin y where a = 1/2K
I compared this to (sin x cos y - cos x sin y) and concluded
1 )cos y = (-a) and cos x = (a) [ Point to note...
I tried to solve the problem just using phi = x - y
this is the worked out solution.
Wanted to check if the method in is acceptable. Solution in the first 3 pages is actual manipulation the remaining are the stability interpretation of the result
Page 1 ...
from the transformation equations we get
x = u +v
y = u -v
so u'=x'+y' and v'=x'-y'
Now the values are put into get the equations
u'= E-cos u sin v (1)
v'= -sin u cos v - K sin 2v (2)
Now setting the system to zero for fixed points
we get...
I get u' = -cos u sin v
so either sinv =0 or cosu = 0 so v =arcsin 0 +- npi , u =arccos 0 +- npi
Ordinarily we take the jacobian of the systems to get eigen values and eigen vectors to state something about the stabiiy of the points.
What do i do in this case ?
Yes that wht i did with phi'=0
but i didnt get points instead getting the question shown above it. Nvm ill put up my whole worked sheet as scans.
typing it wil take an era
Homework Statement
x'= E - sin x + K sin (y-x)
y'= E + sin y + K sin (x-y)
E and K >0
Find fixed points for this system of equations
Homework Equations
This system is the form of coupled oscillators described in Strogatz.
θ1'= ω1 + K sin (θ2-θ1)
θ2'= ω2 + K sin (θ1-θ2)...
Homework Statement
Consider the system of equations : x' = x-y-x^3 and y'=x+y-y^3
a) Draw a phase plot ( Done numericlly program listed here in matlab)
b) Prove analytically that at-least one stable cycle exists ( Used Poincare Bendixon theorem to prove done)
c) Compute the period of...
Do the conclusions of then discussion hold if the concept of mass in special relativity does not hold ? ( A contention held at the end of the article linked above ?
I was thinking on the following lines..
When the battery system is at higher energy that is the constituent particles are...