Attitude Determination by External Vectors in Airplane Free Spin Investigation

The article gives an overview of the methods for determining orientation angles from observations of external reference vectors. To maintain the observability of the kinematic parameters of the free-flying aircraft model motion in a vertical wind tun-nel, we analyzed the methods for determining the finite rotation vector using two, three or more vectors, known in a model body frame, as well as their derivatives. The methods to estimate the reliability of the calculated orientation angles are proposed. The method for estimating the radius of the free-flying model spin is considered.

APPLICATION OF THE “FINITE ROTATION AND DISPLACEMENT” METHOD TO CONTROL THE PARABOLIC ANTENNA

The article deals with the application of the "finite rotation and displacement" method (FRDM) which can find the desired values of the generalized coordinates for the control system of a parabolic antenna. The special manipulator of a sequential structure with sufficient rigidity is used to control the parabolic antenna. The rigidity of this manipulator is ensured by use of links in the form of spherical shells and bearings located along the perimeter of each shell in the rotation plane of each link. It allows to optimally place the material of the manipulator's design and to obtain sufficient rigidity with minimal weight. The manipulator consists of four links connected by fifth class kinematic pairs with an arbitrary inclination of the axes. For this task the antenna's orientation is important without taking into account the small displacement of its position during the process of its orientation. The FRDM method provides both orientation and position. It is based on determining the precise and optimal iterative steps for each degree of mobility, providing maximum approximation to the specified orientation parameters of the parabolic antenna. According to the method's algorithm, the software is developed consisting of subprograms for organizing a general solution of the inverse kinematics for an arbitrary number of links and a particular one for a manipulator in the form of source data. The initial data are the vector model of the manipulator, the values of the structural constraints of the generalized coordinates, and the characteristics of kinematic pairs by type and class

TEST SIMULATION OF «FINITE ROTATION AND DISPLACEMENT» METHOD BY THE EUROPEAN ROBOTIC ARM PASSING THROUGH THE SINGULAR POINTS

The article consider the test simulation of the «finite rotation and displacement» method (FRDM) when the European Robotic Arm (ERA) manipulator is passing through the singular points. The test simulation confirms the method’s efficiency when passing through singular points and shows how to control the manipulator with various manifestations of the singularity. Depending on the type of singularities manifestation the manipulator is controlled in the vicinity of the singular point by means of small changes in its configuration or by limiting and setting specific values to generalized coordinates at the software and hardware level. The FRDM method is designed to solve the inverse kinematics (IK) for sequential-structure manipulators with an arbitrary number of links connected by fifth-class kinematic pairs. The method is based on determining the exact and optimal iterative steps that provide the maximum approximation to the given parameters of the final link for each degree of mobility. The software has been developed that consists of subprograms for organizing a general solution of the IK and a particular one for a particular manipulator in the form of source data according to the algorithm of the method. The initial data are the vector model of the manipulator, the values of the structural constraints of the generalized coordinates and signs of kinematic pairs by type and class.

The New Analytical Algorithm for Determining the Strapdown INS Orientation

The analytical solution of an approximate (truncated) equation for the vector of a rigid body finite rotation has made it possible to solve the problem of determining the quaternion of orientation of a rigid body for an arbitrary angular velocity and small angle of rotation of a rigid body with the help of quadratures. Proceeding from this solution, the following approach to the construction of the new analytical algorithm for computation of a rigid body orientation with the use of strapdown INS is proposed: 1) By the set components of the angular velocity of a rigid body on the basis of mutually — unambiguous changes of the variables at each time point, a new angular velocity of a rigid body is calculated; 2) Using the new angular velocity and the initial position of a rigid body, with the help of the quadratures we find the exact solution of an approximate linear equation for the vector of a rigid body finite rotation with a zero initial condition; 3) The value of the quaternion orientation of a rigid body (strapdown INS) is determined by the vector of finite rotation. During construction of the algorithm for strapdown INS orientation at each subsequent step the change of the variables takes into account the previous step of the algorithm in such a way that each time the initial value of the vector of finite rotation of a rigid body will be equal to zero. Since the proposed algorithm for the analytical solution of the approximate linear equation for the vector of finite rotation is exact, it has a regular character for all angular motions of a rigid body).

Physics from Axioms

We introduce a definition of Time and Photons from four Axioms. Basically you take a 4-dimensional manifold, transform them into two superimposed Riemann Spheres and isolate a circle (call this Pp) in one of the spheres. Then one specifies the circle to turn by a unit amount (the turn is an quantum rotation: turn from state A to state B without visiting the in between states) as measured along the circle, every time the Pp encounters a space point. Space fluctuates and expands so this does not give a static circle Pp. The circle's infinity point stays at the north pole of the Riemann Sphere for any finite rotation since: infinity - constant = infinity. Using this one can define basic spacetime and from basic spacetime, Time can be defined if we require special particles to be in the particles of a clock. We go on to define photons and antiphotons. The model predicts that there is a direction in which photons (from the same process) are never emitted. We continue to define a pi-minus.