Mechanics

Solving Kinematic Problem of Optimal Nonlinear Stabilization of Arbitrary Program Movement of Free Rigid Body

Authors: Chelnokov Y. N., Nelaeva E. I.

The kinematic problem of nonlinear stabilization of arbitrary program motion of free rigid body is studied. Biquaternion kinematic equation of perturbed motion of a free rigid body is considered as a mathematical model of motion. Instant speed screw of body motion is considered as a control. There are two functionals that are to be minimized. Both of them characterize the integral quantity of energy costs of control and squared deviations of motion parameters of a free rigid body from their program values.

Wave Occurrences Mathematical Modeling in Two Geometrically Nonlinear Elastic Coaxial Cylindrical Shells, Containing Viscous Incompressible Liquid

Authors: Blinkov Y. A., Mesyanzhin A. V., Mogilevich L. I.

The investigation of deformation waves behavior in elastic shells is one of the important trends in the contemporary wave dynamics. There exist mathematical models of wave motions in infinitely long geometrically non-linear shells, containing viscous incompressible liquid, based on the related hydroelasticity problems, which are derived by the shell dynamics and viscous incompressible liquid equations in the form of generalized Korteweg – de Vries equations.