Chernova M. Method of analytical mechanics in the problems of the nonlinear drop dynamics

Українська версія

Thesis for the degree of Candidate of Sciences (CSc)

State registration number

0412U006146

Thesis Registration Form

0412U006146.pdf

Applicant for

Specialization

  • 01.02.01 - Теоретична механіка

13-11-2012

Specialized Academic Board

Д 26.206.02

The Institute of Mathematics of NASU

Essay

In the thesis, based on the variational principles of the Hamilton-Ostrogradsky type, the methods of the theoretical mechanics are generalized and developed for the nonlinear dynamics of a drop. An emphasis is placed on nonlinear modal methods which reduce the theoretical analysis to a system of nonlinear ordinary differential equations with respect to generalized coordinates of the mechanical system. The Hamilton-Ostrogadsky variational formalism within the Bateman-Luke action are employed. The Lukovsky-Miles type nonlinear modal equations are derived. An analogy of the potential energy principle was proved for the so-called capillary-acoustical shapes of the levitating drop. A general third-order weakly-nonlinear modal theory is constructed for the axisymmetric drop dynamics.

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