Abstract. Starting from the defining transformations of complex matrices for the SO(4) group, we construct the fundamental representation and the tensor and spinor representations of the group SO(4). Given the commutation relations for the corresponding algebra, the unitary representations of the group in terms of the generalized Euler angles are constructed. These mathematical results help us ...

We consider the Euler type integral associated to the configuration space of points on an elliptic curve, which is an analogue of the hypergeometric function associated to the configuration space of points on a projective line. We calculate the twisted homology group, with coefficients in the local system associated to a power function gα of an elliptic function g, and the intersection form. Ap...

Robust nonlinear control of flexible-joint robots requires that the link position, velocity, acceleration, and jerk be available. In this paper, we derive the dynamic model of a nonlinear flexible-joint robot based on the governing Euler-Lagrange equations and propose extended and unscented Kalman filters to estimate the link acceleration and jerk from position and velocity measurements. Both o...

This paper presents a recursive formulation for the inverse dynamics of a generic twoDegree of Freedom planar parallel manipulator with prismatic actuators, which find applications in positioning, contouring, etc. with high accuracy and precision. The method is based on the Newton-Euler equations of motion and the Decoupled Natural Orthogonal Complement matrices, which relate the angular and li...

We present a high order accurate streamline-upwind/Petrov-Galerkin (SUPG) algorithm for the solution of the compressible Euler and Navier-Stokes equations. The ow equations are written in terms of entropy variables which result in symmetric ux Jacobian matrices and a dimensionally consistent Finite Element discretization. We show that solutions derived from quadratic element approximation are o...

In this paper, the singularity of Euler angles rotation representation in robot pose estimation is overcome. This is accomplished through coordinate system rotating and sign-adjusting of the intrinsic parameter camera matrices. A stereo pair is attached to the robot and the extended Kalman filter is used as a recursive pose estimator. An extensive set of synthetic and real experiments have been...

Analysis of the final phase of the overarm handball throw was carried out by a microcomputerized treatment of photographic images taken simultaneously in two grid layouts. Reflective stickers on the joints of the throwing arm (shoulder, elbow, wrist) allowed the coordinates of these three points to be measured against a reference on the wall. Using a mathematical treatment and Euler matrices, t...

This paper considers the stability of both continuous and discrete time-varying linear systems. Stability estimates are obtained in either case in terms of the Lipschitz constant for the governing matrices and the assumed uniform decay rate of the corresponding frozen time linear systems. The main techniques used in the analysis are comparison methods, scaling and the application of continuous ...

Abstract. Starting from the defining transformations of complex matrices for the SO(4, R) group, we construct the fundamental representation and the tensor and spinor representations of the group SO(4, R). Given the commutation relations for the corresponding algebra, the unitary representations of the group in terms of the generalized Euler angles are constructed. The crucial step for the Barr...

This work is based on EulerSeidel matrices ([8]) which is related to algorithms, combinatorics and generating functions. This method is quite useful to investigate properties of some special numbers and polynomials. In this work we use this method to find out some interesting results of Fubini and Bell polynomials and numbers. Although some results are known in this paper, this method provides ...