- #1

- 7

- 0

_{x}, a

_{y}, a, v, v

_{x}, and v

_{y}are related to a trajectory graph. I guess I just can't wrap my head around it because I think that we should only be able to find these values from a position vs. time graph.

- Thread starter mymabelline
- Start date

- #1

- 7

- 0

- #2

- 7

- 0

- #3

Pythagorean

Gold Member

- 4,214

- 272

You would also plot the nullclines of the system on such a phase plot. Those nullclines (which are lines in a two-dimensional system) tell you exactly where the rate change (dx/dt and dy/dt) are zero. This would be velocity if your system pertains to motion.

So if your trajectory is on either side of the nullcline, this tells you whether it is a positive rate change or a negative rate change (i.e. a positive or negative velocity would indicate direction). And the farther away from the nullcline, the greater the value of that change rate.

But because the nullclines are somehow parameterized on the phase plot (i.e. they're not linear with the variables x and y), you can imagine that the real valued change rates would also have to be parameterized on the line. There's no easy way to do that. You would have to plot all the "non-nullcline" lines. And each of the fixed points are going to have different strengths, which you can only analyze by computing the eigenvalues of the jacobian. So this is not so trivial.

- #4

- 12,121

- 159

- #5

- 7

- 0

- #6

Pythagorean

Gold Member

- 4,214

- 272

- #7

- 12,121

- 159

In your first post, you said nothing about having any equations, or any time values; only a graph of

If you

- Replies
- 4

- Views
- 4K

- Last Post

- Replies
- 4

- Views
- 5K

- Last Post

- Replies
- 9

- Views
- 2K

- Last Post

- Replies
- 22

- Views
- 1K

- Last Post

- Replies
- 2

- Views
- 1K

- Last Post

- Replies
- 4

- Views
- 2K

- Last Post

- Replies
- 1

- Views
- 3K

- Last Post

- Replies
- 12

- Views
- 1K

- Last Post

- Replies
- 5

- Views
- 1K

- Last Post

- Replies
- 0

- Views
- 999