In the case that they are orthogonal at all points where the derivatives are well-defined, we define the Lamé coefficients (after Gabriel Lamé) by
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The name curvilinear coordinates, coined by the French mathematician Lamé, derives from the fact that the coordinate surfaces of the curvilinear systems are curved.
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For instance, a physical problem with spherical symmetry defined in R3 (for example, motion of particles under the influence of central forces) is usually easier to solve in spherical polar coordinates than in Cartesian coordinates.