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 .

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