Methodology of determining of the transfer function of engagement kinematics of accelerations of an aircraft and its elliptic coordinates in alternative representation

In this work, simplified expressions have been obtained that describe the kinematics parameters of the aircraft movement and its accelerations. These expressions are needed to obtain an optimal linear control law in order to provide movement of the aircraft using the hyperbola guidance method with a time difference of arrival navigation system. The key feature of the hyperbola navigation method is the ability to reduce the number of navigation positions by one when the on-board navigation equipment operates in a passive mode, carrying out only the reception of navigation information, like consumers of satellite navigation information.

Methodology of determining of the transfer function of engagement kinematics of accelerations of an aircraft and its elliptic coordinates used for thr guidance based on time difference of arrival

This paper discusses the problem of determining a kinematics (in terms of transfer function, as far as possible) of parameters of the motion of an aircraft expressed in the curvilinear coordinate system and control accelerations expressed in a rectangular coordinate system. Examples of curvilinear coordinate systems using in practice can be polar, biangular, two-center bipolar, elliptic, parabolic cylindrical, spherical, ellipsoidal, coordinate systems. A technique for obtaining a kinematic link for the control problem of an unmanned aerial vehicle in the elliptic coordinate system was described. It allowed to obtain simpler view of the kinematic link which could provide navigation an aircraft along the hyperbola deriving from the time difference of arrival navigation system. It can. As a result, it is possible to reduce the number of the navigation radio beacons.

Solution of two dimensional Stokes flow with elliptical coordinates and its application to permeability of porous media

Analytical developments of the biharmonic equation representing bi-dimensional Stokes flow are realized with elliptic coordinates. It's found that the streamfunction is expressed with series expansions based on Gegenbauer polynomials of first and second kinds with order one Cn1and Dn1. A term corresponding to order n=-1 is added in view to create drag on a body around which the fluid flows. Application to an array of elliptic cylinders is made and the permeability of this medium is determined as a function of porosity.

Analytical solutions of some internal boundary value problems of elasticity for domains with hyperbolic boundaries

An analytical solution of two-dimensional problems of elasticity in the region bounded by a hyperbola in elliptic coordinates is constructed using the method of separation of variables. The stress–strain state of a homogenous isotropic hyperbolic body and that with a hyperbolic cut is studied when there are non-homogenous (non-zero) boundary conditions given on the hyperbolic boundary. The graphs for the numerical results of some test problems are presented.