I should state all linear subspaces for which the solutions for t->inf or t->-inf converge against x=0.

Printable View

- November 20th 2010, 06:55 AMLHeiner
I should state all linear subspaces for which the solutions for t->inf or t->-inf converge against x=0.

- November 20th 2010, 11:15 AMAckbeet
I think I have an idea what you mean. Let's take Now, we don't know the signs of and so we'll have to do different cases depending on which one we have. We may be able to do something clever with the signum function. I'll do the first component for to show you what's going on. We have

The trig functions are not going to either blow up or go to zero. Suppose Then the exponential blows up. Since we can't have that, the only option is if Otherwise, the component blows up. If, on the other hand, then it doesn't matter what and are, the component will go to zero.

Conversely, let's say we are looking at The situation will be precisely the opposite of the previous case. means a blow-up unless and means the component goes to zero regardless of what and are.

Does that help? - November 21st 2010, 01:04 AMLHeiner
yes thank you very much, i thought of that already!

- November 22nd 2010, 05:21 AMAckbeet
So you've got the final answer, then?

- November 27th 2010, 12:27 AMLHeiner
I was wondering how the plot of this system would look like (depending on (a,b) )? But I dont know how to plot it in maple?

Has anybody an idea?

thx - November 29th 2010, 05:12 AMAckbeet
Hmm. Your solution is a space curve in 3 dimensions, with parameter t, right? Any of those CAS's should be able to plot that, although I'm not sure how to do that in Maple. I could probably figure it out in Mathematica. Captain Black is your best bet for MATLAB. I don't know who is especially good at Maple on this forum. I would definitely consult the help manual for information on parametric plotting.

- November 29th 2010, 06:02 AMJester
I know a bit about Maple. What exactly are you trying to plot?