Family of constraint-preserving integrators for solving quaternion equations

A family of numerical time integrators that exactly preserve the constraint of quaternion equations is developed. The constraint-preserving integrators based on the property of the skew-symmetric matrix and the proposed proven theorems are used to improve the accuracy of updating Euler parameters. The stability and accuracy analysis of the generalized constraint-preserving integrators is also discussed. Furthermore, we demonstrate that the proposed integrators are A-stable integrators that are proven to be useful in calculating angular orientations of kinematic and dynamic systems. A numerical example is used to demonstrate the superiority of the proposed integrators.