A new and general fractional Lagrangian approach: A capacitor microphone case study
| Autor: | Amin Jajarmi, Dumitru Baleanu, K. Zarghami Vahid, H. Mohammadi Pirouz, Jihad H. Asad |
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| Rok vydání: | 2021 |
| Předmět: |
Microphone
General kernel function Physics QC1-999 Capacitor microphone system Fractional calculus MathematicsofComputing_NUMERICALANALYSIS General Physics and Astronomy Euler–Lagrange equations Dynamical system Electric charge Displacement (vector) Matrix (mathematics) Nonlinear system Kernel (image processing) Applied mathematics Matrix approximation technique Algebraic number Mathematics |
| Zdroj: | Results in Physics, Vol 31, Iss, Pp 104950-(2021) |
| ISSN: | 2211-3797 |
| DOI: | 10.1016/j.rinp.2021.104950 |
| Popis: | In this study, a new and general fractional formulation is presented to investigate the complex behaviors of a capacitor microphone dynamical system. Initially, for both displacement and electrical charge, the classical Euler–Lagrange equations are constructed by using the classical Lagrangian approach. Expanding this classical scheme in a general fractional framework provides the new fractional Euler–Lagrange equations in which non-integer order derivatives involve a general function as their kernel. Applying an appropriate matrix approximation technique changes the latter fractional formulation into a nonlinear algebraic system. Finally, the derived system is solved numerically with a discussion on its dynamical behaviors. According to the obtained results, various features of the capacitor microphone under study are discovered due to the flexibility in choosing the kernel, unlike the previous mathematical formalism. |
| Databáze: | OpenAIRE |
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