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

Famous quotes containing the words period of, period and/or pulsation:

    “This [new] period of parenting is an intense one. Never will we know such responsibility, such productive and hard work, such potential for isolation in the caretaking role and such intimacy and close involvement in the growth and development of another human being.”
    —Joan Sheingold Ditzion and Dennie Palmer (20th century)

    “Colonial system, public debts, heavy taxes, protection, commercial wars, etc., these offshoots of the period of manufacture swell to gigantic proportions during the period of infancy of large-scale industry. The birth of the latter is celebrated by a vast, Herod-like slaughter of the innocents.”
    —Karl Marx (1818–1883)

    “We are independent of the change we detect. The longer the lever, the less perceptible its motion. It is the slowest pulsation which is the most vital. The hero then will know how to wait, as well as to make haste. All good abides with him who waiteth wisely; we shall sooner overtake the dawn by remaining here than by hurrying over the hills of the west.”
    —Henry David Thoreau (1817–1862)