On the use of quaternions and Euler–Rodrigues symmetric parameters with moments and moment potentials

This paper contains a comprehensive discussion of the use of Euler–Rodrigues symmetric (or Euler symmetric) parameters to parameterize a potential energy function. By exploiting the equivalence of these parameters to unit quaternions, several representations for moments derivable from moment potentials are established. These representations are applied to a system of two rigid bodies connected by an elastic element, and the issue of identification of the potential energy function using moment measurements. It is also shown how the representations can be used to prescribe constraint moments, and how they illuminate the stiffness matrices associated with certain moment potentials.