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| Content Provider | Springer Nature Link |
|---|---|
| Author | Hadjighasem, Alireza Farazmand, Mohammad Haller, George |
| Copyright Year | 2013 |
| Abstract | We show how the recently developed theory of geodesic transport barriers for fluid flows can be used to uncover key invariant manifolds in externally forced, one-degree-of-freedom mechanical systems. Specifically, invariant sets in such systems turn out to be shadowed by least-stretching geodesics of the Cauchy–Green strain tensor computed from the flow map of the forced mechanical system. This approach enables the finite-time visualization of generalized stable and unstable manifolds, attractors and generalized KAM curves under arbitrary forcing, when Poincaré maps are not available. We illustrate these results by detailed visualizations of the key finite-time invariant sets of conservatively and dissipatively forced Duffing oscillators. |
| Starting Page | 689 |
| Ending Page | 704 |
| Page Count | 16 |
| File Format | |
| ISSN | 0924090X |
| Journal | Nonlinear Dynamics |
| Volume Number | 73 |
| Issue Number | 1-2 |
| e-ISSN | 1573269X |
| Language | English |
| Publisher | Springer Netherlands |
| Publisher Date | 2013-02-22 |
| Publisher Place | Dordrecht |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Stability of mechanical systems Non-autonomous dynamical systems Invariant manifolds Coherent structures Vibration, Dynamical Systems, Control Mechanics Mechanical Engineering Automotive Engineering |
| Content Type | Text |
| Resource Type | Article |
| Subject | Ocean Engineering Applied Mathematics Control and Systems Engineering Mechanical Engineering Electrical and Electronic Engineering Aerospace Engineering |
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