Mechanics

The classical problem of optimal control of the attitude maneuver of a spacecraft as a rigid body of arbitrary dynamic configuration under arbitrary boundary conditions for the angular position and angular velocity of a spacecraft without restriction on the control vector function and with a fixed transition time is considered. As a criterion of optimality, the functional of the energy spent on the rotation of a spacecraft is used.

To obtain the deformation matrix of the prismatic finite element at the loading step, taking into account the physical nonlinearity, three variants of physical equations were used. In the first variant, the defining equations of the theory of plastic flow are implemented, according to which the increment of deformations is divided into elastic and plastic parts. The increment of elastic deformations is related to the increments of stresses by Hooke's law.

Within the framework of plane elasticity, the equilibrium problem for an inhomogeneous orthotropic elastic strip under the action of a stamp with a smooth base is investigated. Based on the Fourier transform, a canonical system of differential equations with variable coefficients with respect to transformants of the displacement vector and stress tensor components is constructed.

The bending of an elastic circular three-layer plate asymmetric in thickness by local loads uniformly distributed in a circle in a neutron current is considered. Polyline hypotheses are used to describe the kinematics of the package. Kirchhoff's hypotheses are valid in thin load-bearing layers. In a relatively thick incompressible filler, Timoshenko's hypothesis about the straightness and incompressibility of the deformed normal is fulfilled. The work of the tangential stresses of the filler is taken into account. Deformations are small.