literature

Concerning the nu/N ---> 1/3 resonance. 2. Application of a variational procedure and of the Moser method to the equation d**2 v/dt**2 + (2nu/N)**2 v + 1/2 [Sigma(m=1) b(m) sin 2 mt] v**2 + 0

May, 1959
22 pages
Report number:
  • MURA-459

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0 Citations
Note:
  • Fermilab Library Only
  • [1]
    MURA-452 (April 13,). hereinafter designated as 1
    • L. Jackson Laslett
  • [2]
    Annals of Physics ~3 No.1, 1-48 (January,)--Section 4a, esp. eqns. (4.4) and (4.5), p. 18
    • E.D. Courant
      ,
    • H.S. Snyder
  • [3]
    Jiirgen Moser, Nach. Gott. Akad. (Math. - Phys. KI.) Nr. 6, 87-120
  • [4]
    The computational work was performed with the MURA IBM 704, by means of the DUCK-ANSWER program [J (IBM Program 75), MURA-237 J, with the independent variable, L, of the program identified as 7::
    • N. Snyder
  • [4]
    5 t and with the dependent variable ( fJ or "Y') usually identified as 10 times the dependent variable (v) of eqn. (2). Accordingly, dv/dt is then represented by 0.5 d or 0.5 d rId 1::. The coefficients of the program are then taken to be Sl = S2 ::: - 0.016 (z}IN)2, A3 ::: A15 ::: 0.001, B2 ::: B15 :
    • I. IdZ
    • [4]
      0.002, C3 =C15 ::: 0.0015, with N1 ::: 10, N2 ::: 5, and ~3 = «'15 =
      • [4]
        83 ::: ~15:
        • [4]
          : ~::: r
          • [4]
            5 :
            • [4]
              : O
              • [5]
                If one selects NRK :::: 64, a computational run through an interval At = 31L. requires a total of NE ::: 960 Runge- Kutta integration steps. For Fourier analysis of the results of a DUCK-ANSWER computation, the DUCKNALL program was employed [JOhn McNall, (IBM Program 219), MURA-438 (1958)], this program constituting basically an incorporation into the DUCK-ANSWER program of the FORANAL program [J (IBM Program 52), MURA-228 J. 20 MURA-459
                • N. Snyder