Finite-dimensional modeling of elastic objects (Q2901725)

The great number of publications is devoted studying of stability of balance for elastic rod systems now. Interest to this direction is connected with uses of such systems at modeling of structure of a molecule of acid. The finite-dimensional model of an elastic rod is considered in the given work. Rod systems consider geometrical nonlinearity. The rod is modelled by means of system of Lagrange gyroscopes connected by elastic spherical hinges. Elastic hinges suppose turn on any corner. The general view of components of the moment taking into account randomness of angles of rotation is received. The system of the equations found in work, allows to define corners and to find a spatial configuration of a rod in balance position. Special cases are investigated, parities for stable equilibrium of systems are received.