双欧法与四元数法的应用比较

对解决欧拉方程奇异性的双欧拉和四元数法进行了对比研究，四元数法从理论上讲比较完美，但实际应用中存在较大的累积计算误差，从而影响计算精度；双欧法利用正、反欧拉方程间精华区倒挂关系进行分区交替运算，把精华区扩展到全域，不仅根除了奇异性，而且计算误差小。因此，对于解决欧拉方程奇异性来讲，双欧法要优于四元数法。

Application Comparision of Dual Euler Method and Quaternion Method

This paper studies comparatively dual Euler method and quaternion method which are used for the solution of the singularity of the Euler equation. Quaternion method is good in theory, but it has increasing error in calculation. Therefore it is not accurate. Dual Euler method separates the essential area from the overall calculating area and alternate calculation on the inverse relationship of essence area between the ordinary and reversed Euler equation. The essential area is expanded to the whole area and the singularity is overcomes completely, and it has no error bisically. So, dual Euler method is better than quaternion method in the solution of the singularity of the Euler equation.