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Exact(12)
When they plugged those assumptions into a formula describing the energy of a symmetrical tube of fibers, they came out with the Ponytail Shape Equation.
We derived a mathematical model that relates the two-dimensional kinetic shape equation to the string's physical and dynamic parameters.
The mode shape equation was obtained by using non-linear regression.
A direct analytical solution is presented for the mode shape equation.
In this paper a direct solution of the mode shape equation is presented.
Thus, the shape equation becomes (4), which is the same as the equation that does not include external force.
Similar(47)
The mode shape equations are linear differential equations with regular singularity.
Analytical solutions of the mode shape equations have been derived based on Bessel functions.
Analytical solutions of the two mode shape equations are derived, based on the method of Frobenius.
The mode shapes were extracted, and the eigenvectors were used in determining the mode shape equations using nonlinear regression.
The two mode shape equations are fourth order linear differential equations with variable coefficients and with regular singularity.
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