Coupled differential equations

  • Thread starter tdcaupv
  • Start date
  • #1
7
0

Main Question or Discussion Point

Hi,
I have to modelize the buckling of a column and I've come up with this system:
[tex] N'(x) + N(x) \theta ' (x) \theta (x) - Q \theta ' (x) + f = 0 [/tex]
[tex] Q'(x) + N(x) \theta ' (x) + Q \theta ' (x) \theta (x) = 0 [/tex]

with f a constant

The coefficients (thetas) are not constants.
I've written it as X' = A X + f But I dont know how to diagonalize A since coefficients are not constants.

Thank You for helping me.
 

Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
41,805
932
Actually, it's worse than that. Not only are the coefficients variable, but the second equation includes [itex]\theta \theta'[/itex] so the equations are non-linear and matrix methods cannot be used at all.
 
  • #4
7
0
edit
 
  • #5
lurflurf
Homework Helper
2,426
126
θ is a known function right?
 
  • #6
7
0
Yes.
 
  • #7
lurflurf
Homework Helper
2,426
126
How complicated is θ?
 
  • #8
7
0
Well, i dont know, im a bit lost.
Actually, theta is my slope angle which is very small.
 
  • #9
1,796
53
May I ask why you just don't solve it numerically? I mean really, he didn't say nothing about analytic solution else I'd keep my mouth shut. You know, numerical methods are perfectly fine for the real-world.

So if I may be the practical voice in here: work it first numerically even if you need an analytic solution just to get a handle on it, then do it analytically if you have to.
 
  • #10
7
0
First I need to solve it analytically. Maybe equations are not good. Maybe I should get simplier equations, i dont know ...
 
  • #11
1,796
53
No you don't even if you have to solve it analytically. You know if you're gonna drive your truck in the dark without lights, it's a good idea to first walk the path with a flash light to see if there are any holes and stuf.

I'm tellin' you the right way to approach this: solve it first numerically even if you have to just dream-up initial conditions. Get a handle on it, then attempt to solve it analytically.

Also, I do not believe this is a non-linear system if [itex]\theta(x)[/itex] is known. You effectively have:

[tex]\frac{dN}{dx}=-Ngh+Qh-f[/tex]

[tex]\frac{dQ}{dx}=-Nh+Qhg[/tex]

where g=g(x) and h=h(x) are known functions. Well there you go: I'm dreamin' up g and h, N(0) and Q(0) too, bingo-bango: Numeric solution in hand.
 
Last edited:

Related Threads on Coupled differential equations

  • Last Post
Replies
2
Views
3K
  • Last Post
Replies
5
Views
2K
Replies
1
Views
6K
Replies
5
Views
4K
Replies
0
Views
2K
Replies
1
Views
2K
Replies
4
Views
7K
Replies
13
Views
2K
Replies
17
Views
7K
Replies
2
Views
3K
Top