The dual Euler basis: Constraints, potentials, and Lagrange's equations in rigid-body dynamics

Given a specific set of Euler angles, it is common to ask what representations conservative moments and constraint moments possess. In this paper we discuss the role that a non-orthogonal basis, which we call the dual Euler basis, plays in the representations. The use of the basis is illustrated with applications to potential energies, constraints, and Lagrange's equations of motion.