Analytical solutions of a generalized Duffing-harmonic oscillator by a nonlinear time transformation method

This paper introduces the development of hot-line live working manipulators and gives a new configuration manipulator driven by hydraulic actuator firstly. Then, its forward kinematics equations are derived with homogenous transformation method. Finally, the analytical solutions of its inverse kinematics are solved under the condition that the posture of the end-effector is known and given with z-y-z Euler angles.

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UNITARY TRANSFORMATION APPROACH FOR THE PHASE OF THE DAMPED DRIVEN HARMONIC OSCILLATOR

Modern Physics Letters B ◽

10.1142/s021798490300644x ◽

2003 ◽

Vol 17 (26) ◽

pp. 1365-1376 ◽

Cited By ~ 7

Author(s):

JEONG-RYEOL CHOI

Keyword(s):

Wave Function ◽

Harmonic Oscillator ◽

Unitary Transformation ◽

Operator Method ◽

Classical Equation ◽

Transformation Method ◽

Invariant Operator ◽

Harmonic Oscillators ◽

Parabolic Cylinder ◽

Parabolic Cylinder Function

Using the invariant operator method and the unitary transformation method together, we obtained discrete and continuous solutions of the quantum damped driven harmonic oscillator. The wave function of the underdamped harmonic oscillator is expressed in terms of the Hermite polynomial while that of the overdamped harmonic oscillator is expressed in terms of the parabolic cylinder function. The eigenvalues of the underdamped harmonic oscillator are discrete while that of the critically damped and the overdamped harmonic oscillators are continuous. We derived the exact phases of the wave function for the underdamped, critically damped and overdamped driven harmonic oscillator. They are described in terms of the particular solutions of the classical equation of motion.

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Constructing explicit homoclinic solution of oscillators: An improvement for perturbation procedure based on nonlinear time transformation

Communications in Nonlinear Science and Numerical Simulation ◽

10.1016/j.cnsns.2016.12.010 ◽

2017 ◽

Vol 48 ◽

pp. 123-139 ◽

Cited By ~ 6

Author(s):

Y.Y. Chen ◽

S.H. Chen ◽

W. Zhao

Keyword(s):

Homoclinic Solution ◽

Time Transformation ◽

Perturbation Procedure ◽

Nonlinear Time Transformation

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Construction of sequences of exact analytical solutions for heat diffusion in graded heterogeneous materials by the Darboux transformation method. Examples for half-space

Journal of Physics Conference Series ◽

10.1088/1742-6596/745/3/032059 ◽

2016 ◽

Vol 745 ◽

pp. 032059

Author(s):

J.-C. Krapez

Keyword(s):

Half Space ◽

Darboux Transformation ◽

Analytical Solutions ◽

Heterogeneous Materials ◽

Transformation Method ◽

Heat Diffusion ◽

Exact Analytical Solutions

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EXACT QUANTIZATION RULE AND ITS APPLICATIONS TO PHYSICAL POTENTIALS

International Journal of Modern Physics E ◽

10.1142/s0218301307005661 ◽

2007 ◽

Vol 16 (01) ◽

pp. 189-198 ◽

Cited By ~ 53

Author(s):

SHI-HAI DONG ◽

D. MORALES ◽

J. GARCÍA-RAVELO

Keyword(s):

Harmonic Oscillator ◽

Analytical Solutions ◽

Bound States ◽

Energy Levels ◽

Present Approach ◽

Three Dimensions ◽

One Dimension ◽

Quantization Rule ◽

Exact Quantization Rule ◽

Pseudoharmonic Oscillator

By using the exact quantization rule, we present analytical solutions of the Schrödinger equation for the deformed harmonic oscillator in one dimension, the Kratzer potential and pseudoharmonic oscillator in three dimensions. The energy levels of all the bound states are easily calculated from this quantization rule. The normalized wavefunctions are also obtained. It is found that the present approach can simplify the calculations.

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