Applications of Lodrigues matrix in 3D coordinate transformation

Coordinate Transformation in Nanorobotics

As it is the well known, the nanorobotics is the multidisciplinary field that deals with the controlled manipulation of atomic and molecular-sized objects and therefore sometimes is called molecular robotics. In order to design control algorithm for control of a nanorobot motion in a multipotential field, one should start with the related coordinate transformations. It has been done in this pap...

Simulation of Styrene Polymerization in Arbitrary Cross-Sectional Duct Reactors by Boundary-Fitted Coordinate Transformation Method

The non-orthogonal boundary-fitted coordinate transformation method is applied to the solution of steady three-dimensional conservation equations of mass, momentum, energy and speciescontinuity to obtain the laminar velocity, temperature and concentration fields for simulation of polymerization of styrene in arbitrary cross-sectional duct reactors. Variable physical properties (except for speci...

Freedom in Coordinate Transformation for

A Coordinate Descent Method for Robust Matrix Factorization and Applications

Matrix factorization methods are widely used for extracting latent factors for low rank matrix completion and rating prediction problems arising in recommender systems of on-line retailers. Most of the existing models are based on L2 fidelity (quadratic functions of factorization error). In this work, a coordinate descent (CD) method is developed for matrix factorization under L1 fidelity so th...

Generalized Lorentz Coordinate Transformation

This paper derives equations for generalized Lorentz coordinate transformation based on a simple principle that only the wave equation must be form invariant and valid in both coordinate systems. The usual requirement that the speed of light is a universal constant and thus has an identical value in any inertial coordinate systems is removed. This leads to some interesting conclusions and possi...