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Results pointed out in this paper, are inspired by papers of O.A. Goroshko and
N.P. Puchko, about Lagrange's equations for the multy bodies hereditary
systems by G.M. Savin and Ya. Ya. Ruschitsky, as well as a monography on
rheonimic dynamics written by V. A. Vujii. By using rhelogical body models
for designing deformable rheological hereditary elements with hybrid
rheological elastoviscosic and/or viscoelastic properties, discrete
oscillatory systems with hereditary elements as constraints, are designed,
as systems with one degree of freedom as well as with many degrees of freedom.
For these oscillatory hereditary systems, the integro
differential equations second and/or third kind are composed. The solutions
of these the multy frequency forced vibrations of the hereditary systems.
For example, the rheological properties of the rheonomic coordinate in
the sense of the Vujii's rheonomic coordinate are introduced. Theforce, as
well as the power of the rate of rheological and rheonomic constraints
change are determined.
For the designed discrete hereditary systems with corresponding rheological
and relaxational hereditary elements the integrodifferential equations second
and/or third kind are composed. On the basis of the analysis of the discrete
hereditary oscillatory systems the Goroshko's definition on dynamically
determinated or indeterminated discrete hereditary systems was confirmed.
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