Resonant forcing of nonlinear systems of differential equations

Details Resonant forcing of nonlinear systems of differential equations Resonant forcing of nonlinear systems of differential equations

2008-03-14

arxiv.org/abs/0803.2252v1

Chaos 18, 033118 (2008)

Nonlinear Sciences

Chaotic Dynamics

9 pages, 3 figures

Scientific paper

10.1063/1.2964200

We study resonances of nonlinear systems of differential equations, including but not limited to the equations of motion of a particle moving in a potential. We use the calculus of variations to determine the minimal additive forcing function that induces a desired terminal response, such as an energy in the case of a physical system. We include the additional constraint that only select degrees of freedom be forced, corresponding to a very general class of problems in which not all of the degrees of freedom in an experimental system are accessible to forcing. We find that certain Lagrange multipliers take on a fundamental physical role as the effective forcing experienced by the degrees of freedom which are not forced directly. Furthermore, we find that the product of the displacement of nearby trajectories and the effective total forcing function is a conserved quantity. We demonstrate the efficacy of this methodology with several examples.

Affiliated with

Also associated with

No associations

Rating

Resonant forcing of nonlinear systems of differential equations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Resonant forcing of nonlinear systems of differential equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Resonant forcing of nonlinear systems of differential equations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-438353