Curvilinear coordinates are a coordinate system where the coordinate lines may be curved, allowing for more flexible descriptions of geometries, particularly in complex fluid flow problems. This system is especially useful in situations where traditional Cartesian coordinates can be cumbersome, such as in curved surfaces or in analyzing fluid motion around objects. Curvilinear coordinates can be defined in terms of any smooth curve and can accommodate various shapes and boundaries, facilitating easier mathematical modeling and analysis of fluid dynamics.
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