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Mixed global dynamics of forced vibro-impact oscillator with Coulomb friction
Dynamical Systems · Submitted 14 Mar 2019
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We demonstrate that removal of the viscous friction leads to qualitative modification of the global dynamics.
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The abstract, sentence by sentence
The paper revisits a well-known model of forced vibro-impact oscillator with Amonton-Coulomb friction. In vast majority of the existing studies, this model included also viscous friction, and its global dynamics in the state space is governed by periodic, quasiperiodic or chaotic attractors. We demonstrate that removal of the viscous friction leads to qualitative modification of the global dynamics. Namely, the state space is divided into the regions with "regular" attraction to the aforementioned special solutions, and the regions with profoundly Hamiltonian dynamics. The latter regions contain structures typical for forced Hamiltonian systems: stability islands, extended non-attractive chaotic regions etc. We prove that such local Hamiltonian behavior should occur for phase trajectories with non-vanishing velocity. Stability analysis for the periodic orbits confirms the above statement. It is demonstrated that similar mixed global dynamics can be observed in broader class of models.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The paper revisits a well-known model of forced vibro-impact oscillator with Amonton-Coulomb friction. | background 0.93 | 0.66 | 0.03 | asserted 0.95 |
| s1 | In vast majority of the existing studies, this model included also viscous friction, and its global dynamics in the state space is governed by periodic, quasiperiodic or chaotic attractors. | background 0.99 | 0.03 | 0.04 | asserted 1.00 |
| s2 | We demonstrate that removal of the viscous friction leads to qualitative modification of the global dynamics. | result 0.79 | 0.91 | 0.62 | asserted 1.00 |
| s3 | Namely, the state space is divided into the regions with "regular" attraction to the aforementioned special solutions, and the regions with profoundly Hamiltonian dynamics. | result 0.96 | 0.89 | 0.54 | asserted 1.00 |
| s4 | The latter regions contain structures typical for forced Hamiltonian systems: stability islands, extended non-attractive chaotic regions etc. | result 0.92 | 0.80 | 0.14 | asserted 1.00 |
| s5 | We prove that such local Hamiltonian behavior should occur for phase trajectories with non-vanishing velocity. | result 0.89 | 0.91 | 0.23 | asserted 1.00 |
| s6 | Stability analysis for the periodic orbits confirms the above statement. | result 0.56 | 0.92 | 0.07 | asserted 1.00 |
| s7 | It is demonstrated that similar mixed global dynamics can be observed in broader class of models. | result 0.84 | 0.86 | 0.17 | asserted 0.98 |
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The paper
Original abstract
The paper revisits a well-known model of forced vibro-impact oscillator with Amonton-Coulomb friction. In vast majority of the existing studies, this model included also viscous friction, and its global dynamics in the state space is governed by periodic, quasiperiodic or chaotic attractors. We demonstrate that removal of the viscous friction leads to qualitative modification of the global dynamics. Namely, the state space is divided into the regions with "regular" attraction to the aforementioned special solutions, and the regions with profoundly Hamiltonian dynamics. The latter regions contain structures typical for forced Hamiltonian systems: stability islands, extended non-attractive chaotic regions etc. We prove that such local Hamiltonian behavior should occur for phase trajectories with non-vanishing velocity. Stability analysis for the periodic orbits confirms the above statement. It is demonstrated that similar mixed global dynamics can be observed in broader class of models.
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