Mechanics

Solution of a Problem of Spacecraft’s Orbit Optimal Reorientation Using Quaternion Equations of Orbital System of Coordinates Orientation

Authors: Pankratov I. A., Sapunkov Y. G., Chelnokov Y. N.

The problemof optimal reorientation of the spacecraft’s orbit is solved with the help of the Pontryagin maximum principle and quaternion equations. Control (thrust vector, orthogonal to the orbital plane) is limited inmagnitude. Functional, which determines a quality of control process, is weighted sum of time and impulse (or square) of control. We have formulated a differential boundary problems of reorientation of spacecraft’s orbit. Optimal control laws, transversality conditions, not containing Lagrange multipliers, examples of numerical solution of the problem are given.

Analytical Solution of Linear Differential Error Equations of Strapdown Inertial Navigation System, Functioning in the Normal Geographic Reference Frame, for the Case of an Object, Following the Geographical Equator

Authors: Loginov M. Y., Tkachenko M. G., Chelnokov Y. N.

Analytical solution of linear differential error equations of the strapdown inertial navigation system, functioning in the normal geographic reference frame, for the object, following the Earth equator with constant speed and on the constant height, is derived. The solution is represented in the form, which is convenient for the analysis. The roots of the auxiliary equation are derived in the explicit form. Obtained results can be used, for example, for analysis of the accuracy of strapdown inertial navigation system.

Explicit Models for Flexural Edge Waves in Thin Orthotropic Plates

Authors: Kossovich E. L.

Analysis of flexural edge wave propagation in thin plates is presented. Several problems of semi-infinite plates vibrations are solved. These plates are assumed to be orthotropic. Some basic features of flexural edge wave propagation are found using the constructed explicit parabolic-ellipticmodels. They extract the localized wave contribution into the overall solution.

Explicit Models for Flexural Edge and Interfacial Waves in Thin Isotropic Plates

Authors: Kaplunov J. D., Kossovich E. L., Mukhomodyarov R. R., Sorokina O. V.

Exact solutions for problems of vibrations of isotropic thin elastic plates are presented in the work. Some basic principles of explicit dual parabolic-elliptic models for flexural edge and interfacial waves propagation are revealed. The obtained explicit models extract the contribution of the flexural wave into the full dynamic response. Also, these models reveal a dual parabolic-elliptic nature of the flexural edge and interfacial waves.

Antisymmetric Higher Order Edge Waves in Plates

Authors: Wilde M. V., Kossovich L. Y.

This paper is concerned with the propagation of surface waves localized near the edge of plate (edge waves). Antisymmetric waves in a plate subject to traction free boundary conditions are considered. To study higher order edge waves three-dimensional equations of theory of elasticity are used. Asymptotic analysis is performed, which shows that there are an infinite spectrum of higher order edge waves. For the large values of wave number asymptotics of phase velocities are obtained.