The Experts below are selected from a list of 264 Experts worldwide ranked by ideXlab platform
Marc Delphin Monsia - One of the best experts on this subject based on the ideXlab platform.
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Analysis of a Purely Nonlinear Generalized Isotonic Oscillator Equation
viXra, 2020Co-Authors: Marc Delphin MonsiaAbstract:We perform in this paper a mathematical analysis of a supposed purely nonlinear isotonic Oscillator designed to be a generalization of the Ermakov-Pinney differential Equation. We calculate its exact and general solution. This allows the determination of new periodic solutions to the Ermakov-Pinney Equation as well as non-periodic solutions as complex-valued function. In this context all motions corresponding to this nonlinear isotonic Oscillator are not periodic so it is not consistent to consider such differential Equations with real coefficients as conservative Oscillators which can only have real and periodic solutions like the Harmonic Oscillator Equation.
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A Class of Non-autonomous and Nonlinear Singular Liénard Equations
viXra, 2019Co-Authors: A .b. Yessoufou, Elémawussi Apédo Doutètien, A.v. R. Yehossou, Marc Delphin MonsiaAbstract:A class of non-autonomous and nonlinear singular Lienard Equation is developed by nonlocal transformation of the linear Harmonic Oscillator Equation. It is shown that it includes some Kamke Equations and a nonlinear Equation of the general relativity as special cases.
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A New Trigonometric Function Solution with Amplitude-Dependent Frequency for the Linear Harmonic Oscillator Equation
viXra, 2018Co-Authors: Jean Akande, D. K. K. Adjaï, Y. J. F. Kpomahou, L. H. Koudahoun, Marc Delphin MonsiaAbstract:It is well known that amplitude-dependent frequency features only nonlinear dynamical systems. This paper shows that, however, within the framework of the theory of nonlinear differential Equations introduced recently by the authors of this work, such a property may also characterize the linear Harmonic Oscillator Equation. In doing so it has been found as another major result that the linear Harmonic Oscillator is nothing but the nonlocal transformation of Equation of the free particle motion under constant forcing function.
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Exact Classical and Quantum Mechanics of a Generalized Singular Equation of Quadratic Liénard Type
Journal of Mathematics and Statistics, 2018Co-Authors: L. H. Koudahoun, Jean Akande, Y. J. F. Kpomahou, Damien K. K. Adjaï, Marc Delphin MonsiaAbstract:Authors introduce a generalized singular differential Equation of quadratic Lienard type for study of exact classical and quantum mechanical solutions. The Equation is shown to exhibit periodic solutions and to include the linear Harmonic Oscillator Equation and the Painleve-Gambier XVII Equation as special cases. It is also shown that the Equation may exhibit discrete eigenstates as quantum behavior under Nikiforov-Uvarov approach after several point transformations.
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Solutions of the Duffing and Painlevé-Gambier Equations by Generalized Sundman Transformation
Journal of Mathematics and Statistics, 2018Co-Authors: Damien K. K. Adjaï, Jean Akande, Y. J. F. Kpomahou, L. H. Koudahoun, Marc Delphin MonsiaAbstract:A new approach using the generalized Sundman transformation to solve explicitly and exactly in a straightforward manner the cubic elliptic Duffing Equation is proposed in this study. The method has the advantage to closely relate this Equation to the linear Harmonic Oscillator Equation and to be applied to solve other nonlinear differential Equations. As a result, explicit and exact general periodic solutions to some Painleve-Gambier type Equations have been established and in particular, it is shown that a reduced Painleve-Gambier XII Equation can exhibit trigonometric solutions, but with a shift factor.
Allan D. Pierce - One of the best experts on this subject based on the ideXlab platform.
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Simulations of sonic boom ray tube area fluctuations for propagation through atmospheric turbulence including caustics via a Monte Carlo method
1992Co-Authors: Victor W. Sparrow, Allan D. PierceAbstract:A theory which gives statistical predictions for how often sonic booms propagating through the earth's turbulent boundary layer will encounter caustics, given the spectral properties of the atmospheric turbulence, is outlined. The theory is simple but approximately accounts for the variation of ray tube areas along ray paths. This theory predicts that the variation of ray tube areas is determined by the product of two similar area factors, psi (x) and phi (x), each satisfying a generic Harmonic Oscillator Equation. If an area factor increases the peak acoustic pressure decreases, and if the factor decreases the peak acoustic pressure increases. Additionally, if an area factor decreases to zero and becomes negative, the ray has propagated through a caustic, which contributes a phase change of 90 degrees to the wave. Thus, it is clear that the number of times that a sonic boom wave passes through a caustic should be related to the distorted boom waveform received on the ground. Examples are given based on a characterization of atmospheric turbulence due to the structure function of Tatarski as modified by Crow.
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A Monte‐Carlo approach to the simulation of fluctuations in ray tube areas during propagation through atmospheric turbulence.
The Journal of the Acoustical Society of America, 1991Co-Authors: Victor W. Sparrow, Allan D. PierceAbstract:A simple but approximate theory for the variation of ray tube areas along ray paths leads to the prediction that such areas are the product of the two similar factors, Ψ(x) and Φ(x), each satisfying the generic Harmonic Oscillator Equation, d2Ψ/dx2+f (x)Ψ=0, where the function f (x) (which takes on both positive and negative values) is different for the two factors and depends on the second derivatives of the apparent sound speed with respect to coordinates transverse to the propagation path, and where x corresponds to distance along the path. The theory makes use of a coordinate system, possibly twisting, which follows a central ray and which yields (∂2c/∂y2)/c0 for f (x), where c is an effective sound speed which includes the effect of wind in the direction of ray propagation, c0 is the ambient sound speed. The present paper proceeds from applicable models of turbulence to simulate possible statistical realizations of the random process f (x) and gives the corresponding realizations for the area factor ...
D. P. Mason - One of the best experts on this subject based on the ideXlab platform.
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Non-linear radial oscillations of a thin-walled double-layer hyperelastic cylindrical tube
International Journal of Non-linear Mechanics, 1998Co-Authors: Nikos Roussos, D. P. MasonAbstract:Non-linear radial oscillations of an infinitely long, double-layer, hyperelastic thin-walled cylindrical tube of incompressible material are considered. Conditions are derived on the strain-energy functions of each layer for the radial Equation of motion to reduce to the Ermakov-Pinney Equation. The conditions are satisfied by the Mooney-Rivlin strain-energy function. Non-linear superposition theory for the solution of the Ermakov-Pinney Equation in terms of two linearly independent solutions of the time dependent linear Harmonic Oscillator Equation is reviewed and applied. Exact solutions for the inner radius of the double-layer, thin-walled cylinder are derived for free oscillations and for the Heaviside step loading boundary condition. The radial oscillations of single-layer and double-layer cylindrical tubes of the same thickness and subjected to the same boundary conditions are analysed and compared. The conclusions deduced for the composite cylindrical tube may have application to the dynamics of composite bodies.
Victor W. Sparrow - One of the best experts on this subject based on the ideXlab platform.
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Simulations of sonic boom ray tube area fluctuations for propagation through atmospheric turbulence including caustics via a Monte Carlo method
1992Co-Authors: Victor W. Sparrow, Allan D. PierceAbstract:A theory which gives statistical predictions for how often sonic booms propagating through the earth's turbulent boundary layer will encounter caustics, given the spectral properties of the atmospheric turbulence, is outlined. The theory is simple but approximately accounts for the variation of ray tube areas along ray paths. This theory predicts that the variation of ray tube areas is determined by the product of two similar area factors, psi (x) and phi (x), each satisfying a generic Harmonic Oscillator Equation. If an area factor increases the peak acoustic pressure decreases, and if the factor decreases the peak acoustic pressure increases. Additionally, if an area factor decreases to zero and becomes negative, the ray has propagated through a caustic, which contributes a phase change of 90 degrees to the wave. Thus, it is clear that the number of times that a sonic boom wave passes through a caustic should be related to the distorted boom waveform received on the ground. Examples are given based on a characterization of atmospheric turbulence due to the structure function of Tatarski as modified by Crow.
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A Monte‐Carlo approach to the simulation of fluctuations in ray tube areas during propagation through atmospheric turbulence.
The Journal of the Acoustical Society of America, 1991Co-Authors: Victor W. Sparrow, Allan D. PierceAbstract:A simple but approximate theory for the variation of ray tube areas along ray paths leads to the prediction that such areas are the product of the two similar factors, Ψ(x) and Φ(x), each satisfying the generic Harmonic Oscillator Equation, d2Ψ/dx2+f (x)Ψ=0, where the function f (x) (which takes on both positive and negative values) is different for the two factors and depends on the second derivatives of the apparent sound speed with respect to coordinates transverse to the propagation path, and where x corresponds to distance along the path. The theory makes use of a coordinate system, possibly twisting, which follows a central ray and which yields (∂2c/∂y2)/c0 for f (x), where c is an effective sound speed which includes the effect of wind in the direction of ray propagation, c0 is the ambient sound speed. The present paper proceeds from applicable models of turbulence to simulate possible statistical realizations of the random process f (x) and gives the corresponding realizations for the area factor ...
Abdelhalim Ebaid - One of the best experts on this subject based on the ideXlab platform.
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Approximate periodic solutions for the non-linear relativistic Harmonic Oscillator via differential transformation method
Communications in Nonlinear Science and Numerical Simulation, 2010Co-Authors: Abdelhalim EbaidAbstract:Abstract The relativistic Harmonic Oscillator Equation is a nonlinear ordinary differential Equation given by: x ¨ + ( 1 - x ˙ 2 ) 3 / 2 x = 0 . In this paper, the differential transformation method (DTM) and a relatively new technique, known as aftertreatment technique, are proposed to obtain new approximate periodic solutions for the relativistic Harmonic Oscillator Equation under the initial conditions x ( 0 ) = 0 , x ˙ ( 0 ) = β .
