A rod in one-dimensional space

Let us consider a rod of length L in a one-dimensional space. Here, we label the calculated quantities with the subscript 1. We have 

2 Rigid rod with a random orientation in a d-dimensional space The rod is assumed to be homogeneous it has a length L and zero volume. We associate with it a distribution probability A r) with J dirA(r) = L. The function p(r), corresponding to the fact that the configurations of the rod are random in a d-dimensional space, can be written as follows 

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