Register to reply

Time dependent forcing and nonlinear systems

by nickthequick
Tags: dependent, forcing, nonlinear, systems, time
Share this thread:
nickthequick
#1
Jan18-13, 04:44 PM
P: 52
Hi,

I'm trying to find a toy (i.e. analytic) example of a nonlinear system that has very different behavior for two different types of forcing:

1) [itex]\frac{\partial u(x,t)}{\partial t}+ N(u(x,t)) = F(x) [/itex]

where u(x,t) is the dependent variable, N represents some nonlinear operator with only spatial derivatives and F is a forcing, independent of time.

2)[itex] \frac{\partial u(x,t)}{\partial t}+ N(u(x,t)) = G(x,t) [/itex]


where G now represents a time dependent forcing. I also constrain (1) and (2) to impart the same total amount of momentum to the system in some given time/space interval that we are examining.


I can think of particular scenarios in fluid dynamics where very different behavior can be achieved under similar scenarios to those written above, but I'd like to first think about this for a simpler system, and am currently drawing a blank on examples.

Thanks!

Nick
Phys.Org News Partner Physics news on Phys.org
Vibrational motion of a single molecule measured in real time
Researchers demonstrate ultra low-field nuclear magnetic resonance using Earth's magnetic field
Bubbling down: Discovery suggests surprising uses for common bubbles

Register to reply

Related Discussions
Interested in Chaos Theory, Complex Systems, Nonlinear Systems Academic Guidance 8
Linear/Nonlinear, time-variant/invariant systems Engineering, Comp Sci, & Technology Homework 3
The motion of an object acted on by a time-dependent, position-dependent force? Calculus & Beyond Homework 3
Nonlinear dynamical systems Engineering Systems & Design 0
Nonlinear Systems Precalculus Mathematics Homework 3