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# How can I determine the stability of the equilibrium points of this 2nd-order system? watch

1. Suppose you had a second order system of the form

Where is a 2x2 matrix with real entries. For example, you may have

In which case the system could be written as

Now suppose that this system has an equilibrium point at . How might I determine the stability of this point?

Thanks
2. (Original post by Brian Moser)
Suppose you had a second order system of the form

Where is a 2x2 matrix with real entries. For example, you may have

In which case the system could be written as

Now suppose that this system has an equilibrium point at . How might I determine the stability of this point?

Thanks
Do you have access to a standard textbook such as Strogatz (Chapter 5)? If so, you can get the answer straight out of there. - or see wikipedia.
3. (Original post by Gregorius)
Do you have access to a standard textbook such as Strogatz (Chapter 5)? If so, you can get the answer straight out of there. - or see wikipedia.
So, am I correct in interpreting that as, if both the eigenvalues of A are positive, it is an unstable point, and if they're both negative, it is a stable point?
4. (Original post by Brian Moser)
So, am I correct in interpreting that as, if both the eigenvalues of A are positive, it is an unstable point, and if they're both negative, it is a stable point?
Yes, although it's more usual to classify via the trace and determinant as you then pick up the saddle points - and you can differentiate better between the types of unstable and stable behaviour.
5. (Original post by Gregorius)
Yes, although it's more usual to classify via the trace and determinant as you then pick up the saddle points - and you can differentiate better between the types of unstable and stable behaviour.
How many horse riding puns can you make in a lecture on saddle points and stability?
6. (Original post by Zacken)
How many horse riding puns can you make in a lecture on saddle points and stability?
A little off topic but I thought you might enjoy these.
7. (Original post by joostan)
A little off topic but I thought you might enjoy these.
Oh my god, that's hilarious. I've got the first two so far, will try demystifying the rest.
8. (Original post by joostan)
A little off topic but I thought you might enjoy these.
I've got all but one.

Spoiler:
Show

Going right to left, top to bottom:

Snakes on a Plane

Independence Day

? The only one I can figure out. My best (bad) guess is Something about Mary!

Paths of Glory

8 mile. (Nice thing about fibonacci numbers, is they approximate the conversion miles -> km. 8 mi ~ 13 km, 13 mi ~ 21 km, etc.)

The Matrix (? Might be something else/more specific, but I'm quite sure it's just the matrix)

Field of Dreams

Alpha and Omega

Floor 13

Sum of all fears.

9. (Original post by FireGarden)
...
The joys of having too many female friends. Mean girls.
10. (Original post by FireGarden)
I've got all but one.
Spoiler:
Show

Going right to left, top to bottom:

Snakes on a Plane

Independence Day

? The only one I can figure out. My best (bad) guess is Something about Mary!

Paths of Glory

8 mile. (Nice thing about fibonacci numbers, is they approximate the conversion miles -> km. 8 mi ~ 13 km, 13 mi ~ 21 km, etc.)

The Matrix (? Might be something else/more specific, but I'm quite sure it's just the matrix)

Field of Dreams

Alpha and Omega

Floor 13

Sum of all fears.

(Original post by Zacken)
The joys of having too many female friends. Mean girls.
That's brilliant

Also Zacken
Spoiler:
Show
jk lol
11. You lot might enjoy this:

as well.
12. (Original post by Zacken)
You lot might enjoy this:

as well.

Still thinking about some of them, though

I've got
Spoiler:
Show

Bottom right: Need for Speed
Top right: Gravity
Pink box: Divergent
Yellow box: Limitless
13. (Original post by Indeterminate)

Still thinking about some of them, though

I've got
Spoiler:
Show

Bottom right: Need for Speed
Top right: Gravity
Pink box: Divergent
Yellow box: Limitless
Spoiler:
Show
Bottom left: 21 and Over
Blue box: Step Up? idk this one
14. (Original post by Indeterminate)

Still thinking about some of them, though

I've got
Spoiler:
Show

Bottom right: Need for Speed
Top right: Gravity
Pink box: Divergent
Yellow box: Limitless
(Original post by Student403)
Spoiler:
Show
Bottom left: 21 and Over
Blue box: Step Up? idk this one
Ooh, you're good at this!
15. (Original post by Student403)
Spoiler:
Show
Bottom left: 21 and Over
Blue box: Step Up? idk this one
Spoiler:
Show
Never heard of '21 and Over'
Step Up has to be right, surely?

Top left: Edge of Tomorrow
16. (Original post by Indeterminate)
Spoiler:
Show
Never heard of '21 and Over'
Step Up has to be right, surely?

Top left: Edge of Tomorrow
Ooh, I just watched Edge of Tomorrow recently.

Also, you haven't watched 21 and Over?! You need to!!
17. (Original post by Indeterminate)
Spoiler:
Show
Never heard of '21 and Over'
Step Up has to be right, surely?

Top left: Edge of Tomorrow
Nice one!!
Spoiler:
Show
Grey box: The Grey
18. (Original post by Student403)
Nice one!!
Spoiler:
Show
Grey box: The Grey
Identity thief!
19. (Original post by Student403)
Nice one!!
Spoiler:
Show
Grey box: The Grey
Getting there now
Spoiler:
Show

The other blue box: Identity Thief
20. (Original post by Zacken)
Identity thief!
(Original post by Indeterminate)
Getting there now
Spoiler:
Show

The other blue box: Identity Thief
Notice me senpai

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