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.
The general coordinate system.
The obtained representations are invariant under general coordinate transformations.
All the strain measures discussed here are formulated in the general coordinate-free form.
We next state the strong conservation form for time-dependent general coordinate systems.
A mechanical system can be described by general coordinates q = ( q 1, …, q d ).
2, we consider a general coordinate transformation, which recasts the dynamics of a system in terms of phase-amplitude coordinates.
Formulas of the numerical method are presented for the finite-volume discretization of the Navier-Stokes equations in general coordinates.
Two general coordinate systems have been used extensively in computational fluid dynamics: the Eulerian and the Lagrangian.
