Analytical dynamics of discrete hereditary systems (Q2724153)

The monograph yields a theory of analytic dynamics of discrete hereditary systems, ``hereditary oscillators'', consisting of mass points (rigid bodies) connected by means of deformable elements having properties of generalized standard hereditary bodies. The masses of these connection elements are negligible.NEWLINENEWLINELagrange equations for ``dynamically determinate'' and for ``dynamically indeterminate'' hereditary discrete systems are derived, as well as integro-differential equations of rheological and of relaxation forms. Vector equations for discrete mass point systems with rheonomic constraints and with standard hereditary connection elements are obtained by applying ``rheonomic coordinate method''.NEWLINENEWLINEThe subject matter is divided into nine chapters: 1. Previous foundations of mechanics of hereditary systems, 2. Hereditary systems with one degree of freedom, 3. Discrete hereditary systems with several degrees of freedom -- Lagrange equations, 4. Dynamic equations for two bodies with hereditary connection, 5. Vector dynamic equations for discrete hereditary systems -- method of rheonomic coordinate, 6. Free oscillations of discrete hereditary chain system, 7. Forced oscillations for discrete hereditary chain system, 8. Discrete thermorheologic hereditary system, 9. Discrete piezo-rheologic hereditary system. Conclusions.