# Simplification of vertices and dihedral angle relations of a polygonal chain

I am trying to understand the generation of Cartesian coordinates of polygonal system or poly line with fixed bond angles and fixed link lengths. I assumed the bond angle to be the same and link lengths to be one unit. The relations connecting Cartesian coordinates and Dihedral angles are quite complex, which is in fact product of rotation matrices. Is there any way I can simplify those finite product rotation matrix in such problem? Is there any approximation methods employed to the product of rotations matrices so that I can study the vertex-vertex interactions? Can you please suggest some references in this regard?

• I don't understand what you want to do. – nicoguaro Feb 12 '20 at 14:21