Sentence examples for general coordinates from inspiring English sources

However, a generalization of this expression useful for general coordinates (not just Cartesian) and general spaces (not just Euclidean) takes the form: :ds^2 = \sum_{i,j}^n g_{ij}\, dx_i\, dx_j where gij is called the metric tensor.

Our initial motivation to study more general coordinates comes from the idea to generate problem-oriented coordinate systems for astrophysical numerical calculations.

Formulas of the numerical method are presented for the finite-volume discretization of the Navier-Stokes equations in general coordinates.

Using rotation matrices, the angle between yarns and longitudinal direction has been incorporated in general coordinates of the model.

Relationships among the parameters are given for general coordinates including fixed and moving coordinates and for any definition of wave celerity.

A class of high resolution kinetic beam schemes in multiple space dimensions in general coordinates system for the ideal quantum gas is presented for the computation of quantum gas dynamical flows.

All the strain measures discussed here are formulated in the general coordinate-free form.

Two general coordinate systems have been used extensively in computational fluid dynamics: the Eulerian and the Lagrangian.

The model equations are the three-dimensional, free surface, primitive equations with orthogonal curvilinear coordinates in the horizontal and the new general coordinate in the vertical.

In contrast to traditional layered isopycnal models, in which along-layer density gradients vanish, general coordinate approaches must deal with extra terms.

The general coordinate system.