Jacobian Matrix

This research report compares two approaches to kinematics modeling of articulated rovers with active suspension systems. The first method is based on taking the derivative of transformation matrices of various frame, and equating it with those of a general body in motion to obtain the Jacobian matrix of the rover. The second method is based on position and orientation velocity

The basis of comprehension of power-flow problems obtained from lectures, lecture slides and subject book. Circuit built and simulated in the Power World program, and then the analytical solution obtained using the theoretical knowledge. Finally, both answers were compared with each other and the difference in the figures were deducted and discussed elaborately.

Bài báo vẽ ra một bức tranh toàn cảnh về việc giải thích hàm mật độ xác suất của hàm phân phối xác suất Gauss. Sử dụng các kiến thức tích phân hai lớp sơ cấp và phương pháp biến đổi về tọa độ cực, chúng tôi tóm tắt các quá trình biến đổi có hệ thống nhằm cung cấp kiến thức cơ sở để tiếp tục xây dựng các nghiên cứu tiếp theo.

In this paper we present a particular architecture of parallel robots which has six-degrees-of-freedom (6-DOF) with only three limbs. The particular properties of the geometric and kinematic models with respect to that of a classical parallel robot are presented. We show that inverse problems have an analytical solution. However, to solve the direct problems, an efficient numerical procedure which needs

A fast, matrix-free implicit method has been developed to solve the three dimensional compressible flow problems on unstructured meshes. An approximate system of linear equations arising from the Newton linearization is solved by the GMRES (Generalized Minimum RESidual) algorithm with a LU-SGS (Lower-Upper Symmetric Gauss-Seidel) preconditioner. A remarkable feature of the present GMRES+LU-SGS method is that the storage of the Jacobian matrix can be completely eliminated by approximating the Jacobian with numerical fluxes, resulting in a matrix-free implicit method. The developed method has been used to compute compressible flows around 3D complex aerodynamic configurations for a wide range of flow conditions, from subsonic to supersonic. The numerical results indicate that the use of the GMRES+LU-SGS method leads to a significant increase in performance over the best current implicit methods, GMRES+ILU and LU-SGS, while maintaining memory requirements competitive to its explicit counterpart.

Magnetostatic permeability tomography is an imaging technique that attempts to reconstruct the permeability distribution of an object using magnetostatic measurement data. The data for image reconstruction are external magnetic field measurements on the surface of the object due to an applied magnetostatic field. Theoretically, the normal and tangential components of the magnetic field in the surface uniquely define the internal

This paper deals with the calculation of partial derivatives (w.r.t. the independent variables, x) of a vec of dependent variables y which satisfy a system of nonlinear equations g(u(x), y) = 0 . A number of authors have suggested that the forward accumulation method of automatic differentiation can be applied to a suitable iterative scheme for solving the nonlinear system

An efficient algorithm has been developed for 1D resistivity inversion problem using both first- and second-order derivatives, which are computed analytically. The second-order derivative matrix, which is not used in the OCCAM's inversion, has been incorporated into the algorithm employing analytical expressions. Computation of complicated second-order derivatives in each iteration is circumvented by a new algorithm. These modifications result in stable convergence of the OCCAM's inversion and in general, better misfit can be achieved specially for smoothing parameter, μ<1. The modified inversion algorithm, coded in MATLAB was tested using two synthetic Schlumberger resistivity sounding examples. Its application has been illustrated with field data from south India.

This paper presents a new approach for the determination of 3 - RPR planar parallel robot assembly modes. In this approach, the parallel robot is considered as a multi robot system. The segments are then regarded as serial robots moving a common load. The proposed approach is ...