Sliding solutions of second‐order differential equations with discontinuous right‐hand side

Silva, Clayton E. L. da; Silva, Paulo Ricardo da; Jacquemard, Alain

doi:10.1002/mma.4387

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2018

2024

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Cited by 9 publications

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“…Several periodic orbits were obtained in closed form, and symmetry in space and time was proved for some of these periodic solutions. For more discussion about discontinuous system, refer to [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Analysis of Discontinuous Dynamical Behaviors of a Friction-Induced Oscillator with an Elliptic Control Law

Fan

Liu

et al. 2018

Mathematical Problems in Engineering

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This paper develops the passability conditions of flow to the discontinuous boundary and the sticking or sliding and grazing conditions to the separation boundary in the discontinuous dynamical system of a friction-induced oscillator with an elliptic control law and the friction force acting on the mass through the analysis of the corresponding vector fields and -functions. The periodic motions of such a discontinuous system are predicted analytically through the mapping structure. Finally, the numerical simulations are given to illustrate the analytical results of motion for a better understanding of physics of motion in the mass-spring-damper oscillator.

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