In geometry, curvilinear coordinates are a coordinate system for Euclidean space in which the coordinate lines may be curved. Commonly used curvilinear coordinate systems include: rectangular, spherical, and cylindrical coordinate systems. These coordinates may be derived from a set of Cartesian coordinates by using a transformation that is locally invertible at each point. This means that one can convert a point given in a Cartesian coordinate system to its curvilinear coordinates and back. The name curvilinear coordinates, coined by the French mathematician Lamé, derives from the fact that the coordinate surfaces of the curvilinear systems are curved.
Orthogonal curvilinear coordinates in 3 dimensions
Vector calculus
Covariant and contravariant bases
Integration
Generalization to ''n'' dimensions
Transformation of coordinates
Vector and tensor algebra in three-dimensional curvilinear coordinates
Tensors in curvilinear coordinates
Vector and tensor calculus in three-dimensional curvilinear coordinates
Fictitious forces in general curvilinear coordinates