GROP-CANONICAL METHOD OF AVERAGING FOR STRONGLY NON-LINEAR MECHANICAL SYSTEMS CLOSE TO EXACTLY INTEGRABLE

Authors

  • Yu. V. Chovnyuk ,
  • I. M. Sivak

Abstract

Justified the canonical method of averaging for strongly non-linear mechanical systems close to the exactly integrable. The use of variables grop-action taken in the practice of quantum-mechanical calculations. The analysis of the movement of the flexible shaft with an unbalanced disc/drum, symmetrically located with respect to the supports.

So considered in this case study of the oscillations of the flexible shaft with symmetrically (relative to its supports) of the saturated disc/drum shows that finding a common solution of nonlinear canonical system involves rather cumbersome calculations when finding the parameters of the canonical transformations.

In some cases, apparently, more simple solution could be perform a canonical transformation on the principle of averaging.

References

Punkar', A. (1972). Yzbrannye trudy [Selected works]. M.: Nauka, T. 2, 961.

Boholyubov, N. N. (1945). O nekotorykh statystycheskykh metodakh v matematycheskoy fyzyke [On some statistical methods in mathematical physics]. K.: AN USSR, 137.

Boholyubov, N. N., Mytropol'skyy, Yu. A. (1963). Asymetrycheskye metody v teoryy nelyneynykh kolebanyy [Asymmetric methods in the theory of nonlinear oscillations]. M.: Fyzmat, 410.

Hrobov, V. A. (1982). Teoryya kolebanyy mekhanycheskykh system [Theory of oscillations of mechanical systems]. K.: Vyshcha shkola, 183.

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Published

2016-12-28

Issue

No. 251 (2016)

Section

Статті

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