Mechanics

Slot of Variable Width in a Hub of Friction Pair

Authors: Mirsalimov V. M., Akhundova P. E.

Plane problem of fracture mechanics for a hub of a friction pair is studied. It is suggested that near the rough friction surface, the hub has a rectilinear slot of variable width. The slot width is comparable with elastic deformations. A criterion and a method for solving the inverse problem of mechanics of contact fracture on definition of displacement function of the hub external contour points in a friction pair with regard to the temperature drop and irregularities of the contact surface in friction pair components is given.

Investigation of the Problem of Optimal Correction of Angular Elements of the Spacecraft Orbit Using Quaternion Differential Equation of Orbit Orientation

Authors: Kozlov E. A., Chelnokov Y. N., Pankratov I. A.

In this paper we consider the problem of optimal correction of angular elements of the spacecraft orbit. Control (jet thrust vector orthogonal to the plane of the orbit) is limited by absolute value. The combined quality functional characterizes the amount of time and energy consumption. With the help of the Pontryagin maximum principle and quaternion differential equation of the spacecraft orbit orientation, we have formulated differential boundary value problem of correction of the angular elements of the spacecraft orbit.

Nonlinear Waves Mathematical Modeling in Coaxial Shells Filled with Viscous Liquid

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

There exist wave motion mathematical models in infinitely long geometrically nonlinear shells filled with viscous incompressible liquid. They are based on related hydroelasticity problems, described by dynamics and viscous incompressible liquid equations in the form of generalized KdV equations. Mathematical models of wave process in infinitely long geometrically nonlinear coaxial cylindrical shells are obtained by means of the small parameter perturbation method.