Abstract
In search of nonlinear oscillations, we envision a 3D elliptic curva-ture-dependent nonuniform charge distribution to creating an electric field along the symmetry axis causing a massive point-like charged particle placed on the symmetry axis to oscillate in a delayed/hesitant nonlinear mode. The charge distribution is a 3D twisted line creating nontrivial electric field causing an unexpected oscillation that is non-orthodox defying the common sense. Calculation of this research flavored investigation is entirely based on utilities accompanied with Computer Algebra Systems (CAS) especially Mathematic [1]. The characteristics of the delayed oscillations in addition to embodying classic graphics displaying the time-dependent kinematic quantities are augmented including various phase diagrams signifying the nonlinear oscillations. The output of our investigation is compared to nonlinear non-delayed oscillations revealing fresh insight. For comprehensive understanding of the hesitant oscillator a simulation program is crafted clarifying visually the scenario on hand.
Highlights
In search of nonlinear oscillations, we envision a 3D elliptic curvature-dependent nonuniform charge distribution to creating an electric field along the symmetry axis causing a massive point-like charged particle placed on the symmetry axis to oscillate in a delayed/hesitant nonlinear mode
To quantifying the mathematical challenges such as calculation of the electrostatic force we justified that the routine classic approach was fruitless
We showed direct application of the computational utilities of the Computer Algebra Systems (CAS) have short-comings and CPU expensive
Summary
We begin with displaying the scenario on hand. Figure 2 shows a segment of an elliptic-based cylinder. The tail of the vector slides along the rim of the contour and its head points to the shown dot on the symmetry axis. By integrating the inverse length of the arrow, the integration sweeps and collects the contributions of the differential charges This feature is built in the shown animation where the slider φ runs over one complete cycle. Because the charge distribution on the 3D contour shown in Figure 2 is curvature-dependent, it is not uniform, first we identify the curvature function for later use. This function is given by [4], r′× r′′ curvature =. The spikes are indicatives of the sharp twists, i.e., the
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