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An integrable BC(n) Sutherland model with two types of particles J. Math. Phys. 52, 103506 (2011) Fractional curve flows and solitonic hierarchies in gravity and geometric mechanics J. Math. Phys. 52, 053514 (2011) Optimal control of underactuated mechanical systems: A geometric approach Cauchy's formula which relates the mean chord length ͑isotropic uniform random chords͒ of a convex body in R n with its volume and surface is extended to the case of nonconvex bodies in the framework of integral geometry. This allows us to generalize the extended Cauchy's formula recently discovered by Blanco and Fournier ͓Europhys. Lett. 61 ͑2͒, 168 ͑2003͔͒, in the field of diffusive random walks, to nonconvex bodies. Monte Carlo simulations illustrate these points in R 2 and in R 3 .

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The analytical expression of the correlation function γ(r) for the cuboid with edges a, b and c is established. The calculation is based on the chord‐length distribution. Details of these structure functions at essential r positions are analysed, including higher derivatives of the correlation function at the maximum chord length. The result was checked on closer analysis of the corresponding scattering intensity I(h) and its asymptotic behaviour I∞(h).

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