Toda Oscillator - Period of Pulsation

Period of Pulsation

The period of pulsation is increasing function of the amplitude .

At, the period ~T(\gamma)=2\pi
\left( 1 + \frac{\gamma^2} {24} + O(\gamma^4)
\right)
~

At, the period ~T(\gamma)=
4\gamma^{1/2}
\left(1+O(1/\gamma)\right) ~

In the whole range, the period and the frequency can be approximated with


k_\text{fit}(\gamma)=
\frac{2\pi}
{T_\text{fit}(\gamma)}=

\left(
\frac
{
10630
+ 674\gamma
+ 695.2419\gamma^2
+ 191.4489\gamma^3
+ 16.86221\gamma^4
+ 4.082607\gamma^5 + \gamma^6
}
{10630 + 674\gamma + 2467\gamma^2 + 303.2428 \gamma^3+164.6842\gamma^4 + 36.6434\gamma^5 + 3.9596\gamma^6 +
0.8983\gamma^7 +\frac{16}{\pi^4} \gamma^8}
\right)^{1/4}

with at least 8 significant figures. The relative error of this approximation does not exceed .

Read more about this topic:  Toda Oscillator

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