Non-linear argumental oscillators: Stability criterion and approximate implicit analytic solution |
| |
| Institution: | 1. Université Paris-Est, Laboratoire Navier (UMR 8205), CNRS, Ecole des Ponts ParisTech, IFSTTAR, F-77455 Marne La Vallée, France;2. Université Paris-Est, MAST, SDOA, IFSTTAR, F-77447 Marne La Vallée, France;1. Center for Dynamics, Department of Mathematics, TU Dresden, D-01062 Dresden, Germany;2. Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland;3. Facultad de Ciencias Naturales y Matemáticas, Escuela Superior Politécnicadel Litoral, Km. 30.5 Via Perimetral, Guayaquil, Ecuador;4. Potsdam Institute for Climate Impact Research (PIK), 14473 Potsdam, Germany;5. Department of Physics, Humboldt University, 12489 Berlin, Germany;1. Faculty of Mathematics and Physics, Charles University in Prague, Sokolovská 83, Praha 8 – Karlín CZ 186 75, Czech Republic;2. Texas A&M University, Department of Mechanical Engineering, 3123 TAMU, College Station, TX 77843-3123, United States of America;1. Key Laboratory of Numerical Simulation of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang, Sichuan 641112, PR China;2. Department of Mathematics, Shanghai Jiao Tong University, Shanghai, 200240, PR China;1. Department of Mathematics G. Castelnuovo, Sapienza Roma University, Roma, Italy;2. In Unam Sapientiam, Roma, Italy;3. IAPS, Istituto Nazionale di Astrofisica INAF, Roma, Italy;4. IASF, Istituto Nazionale di Astrofisica INAF, Palermo, Italy;5. INFN, Sezione Roma1, Roma, Italy |
| |
| Abstract: | The behaviour of a space-modulated, so-called “argumental” oscillator, is studied. The oscillator is submitted to an external harmonic force, which is amplitude-modulated by the oscillator's position in space. An analytic expression of a stability criterion is given. Using the averaging method, an integrating factor and a Van der Pol representation in the (amplitude, phase)-space, an exact implicit analytic solution is given when there is no damping, and an approximate implicit analytic solution is given when there is damping, allowing the plotting of the separatrix curve. An attractor is identified. |
| |
| Keywords: | Non-linear Argumental oscillator Spatial modulation Analytic solution Stability criterion Van der Pol representation |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
