ON THE EULER PARAMETER CONSTRAINT
Academic Article
Overview
Additional Document Info
View All
Overview
abstract
A disadvantage of Euler parameter attitude description is the Euler parameter constraint, i.e., the sum of the squares of the four Euler parameters is equal to unity. Although this constraint can be used as a check on the accuracy of numerical computation, it seems to complicate the formulation of equations of motion by increasing the dimension of the state space due to the need for a Lagrange multiplier to account for the constraint. One can easily justify the increase in the number of coordinates due to the avoidance of singularities in the attitude description. The need for the Lagrange multiplier is the subject of this note. The Euler parameter constraint is examined in two situations: i) derivation of Lagrangian equations of motion of a rigid body with respect to its center of mass and ii) formulation of optimal control necessary conditions for systems using Euler parameter kinematics. In the first instance, the constraint force is shown to be zero and in the second, the optimal control is shown to be independent of the Lagrange multiplier corresponding to the Euler parameter equality constraint.
