Unit Length - Curvilinear Coordinates

Curvilinear Coordinates

In general, a coordinate system may be uniquely specified using a number of linearly independent unit vectors equal to the degrees of freedom of the space. For ordinary 3-space, these vectors may be denoted . It is nearly always convenient to define the system to be orthonormal and right-handed:

where δ_ij is the Kronecker delta (which is one for i = j and zero else) and is the Levi-Civita symbol (which is one for permutations ordered as ijk and minus one for permutations ordered as kji).