#MATHEMATICA 7 FIT NONLINEAR CODE#
#MATHEMATICA 7 FIT NONLINEAR WINDOWS#

In metric units it is 8.99 Г— 10 9 Nm 2/C 2.ДЇor a chosen separation height z, integrating (2) applying Mathematica result a complicated almost useless CPU expensive expression, the same is true applying Maple. The k is the electrostatic coupling constant, Here, q 1 and q 2 are the charges of the lower and the upper rings, respectively. The physical quantity of interest is the electrostatic potential energy, Here, R, and r are the radii of the lower and upper circles: О±, and ОІ are their azimuthal angles, respectively. Assuming analytically this goal is achievable the output of the integration being a function of separation distance is to be differentiated with respect to the separation distance result the interactive force between the rings. And because the charges are distributed on each ring, the latter procedure for a chosen separation distance between the rings requires double integration over azimuthal angles of each ring.

Intuitively speaking any physical quantity such as electrostatic potential energy comes about from summing a distance dependent expression between these two points, Mathematical Analysis- Mathematica Codes-SimulationДЄs shown in Figure 1 the 3D slanted line connects virtually a differential charge length located at point p 1 on the lower ring to a similarly characterized differential charged length on the upper ring, p 2. The bottom ring is clamped on a horizontal support while the upper one is placed above it along the mutual symmetry z-axis.Дў. Depicts two parallel charged rings of different sizes. For clarification of the issues on hand Figure 1 assists depicting the scenario.ДЇigure 1. Information cited in is confined to issues such as electrostatic potential of a charged ring along its symmetry axis, so the challenge is to formulate the needed quantities of the symmetry axis. Contemplating these two we favored the latter.

The former requires calculation of the electric field of the bottom ring at off axis region where the floating ring is at, where the latter calls for evaluation of associated electrostatic potential. The latter requires a methodology, meaning either the mutual interactive force between the rings are to be considered or from energy point of view of their electrostatic potential energy. To quantify the oscillations conducive to the relevant quantities such as: frequency, period, and amplitude, one needs to establish the equation of motion. One would also speculate because of the nature of the charged ring-ring interaction, the oscillation would be nonlinear. Adjusting the relevant physical parameters makes it feasible to balance these two forces making the latter motionless yielding to the equilibrium along the vertical axis, and therefore, intuitively speaking dropping or pushing the floating charged ring above or below the equilibrium in the absentee of non-conservative agents such as air friction results in stable oscillations. The floating ring being massive gets pull down by its weight. Charging both rings positively (negatively) creates repulsive electrostatic force. The project as briefly outlined in the abstract concerns with the oscillations of a charged ring that is placed horizontally floating above another charged ring clamped on a horizontal table along their common vertical symmetry axis. Here in this investigating research article as a sample example we show how we have extended a topic that is hardly discussed in both references and how we have intertwined the analysis in the spirt of a mathematical physics issue with a Computer Algebra System (CAS), Mathematica. The same comment is true for popular mathematical physics texts e.g. The incompleteness of the topics provides opportunities to augment the domain of interest contributing to enriching physics.

#MATHEMATICA 7 FIT NONLINEAR WINDOWS#

Is there a way to fix this? I am using Mathematica version 12.1.1 on Windows 10.Reviewing and instructing off the popular undergraduate and graduate college physics texts reveal the incompleteness of the topics covered in many areas of physics such as issues in electrostatic. The command fit works just fine but fit returns error messages Power::infy: Infinite expression 1/0.

#MATHEMATICA 7 FIT NONLINEAR CODE#

Here in the code I am currently working on. I am doing some nonlinear regression using NonlinearModelFit function.

Mathematica 7 fit nonlinear