Sherif Karim, Nachbagauer Karin, Steiner Wolfgang
Johannes Kepler University of Linz, Altenbergerstr. 69, 4040 Linz, Austria.
Faculty of Engineering and Environmental Sciences, University of Applied Sciences Upper Austria, Stelzhamerstr. 23, 4600 Wels, Austria.
Nonlinear Dyn. 2015;81(1-2):343-352. doi: 10.1007/s11071-015-1995-3. Epub 2015 Feb 28.
Many models of three-dimensional rigid body dynamics employ Euler parameters as rotational coordinates. Since the four Euler parameters are not independent, one has to consider the quaternion constraint in the equations of motion. This is usually done by the Lagrange multiplier technique. In the present paper, various forms of the rotational equations of motion will be derived, and it will be shown that they can be transformed into each other. Special attention is hereby given to the value of the Lagrange multiplier and the complexity of terms representing the inertia forces. Particular attention is also paid to the rotational generalized external force vector, which is not unique when using Euler parameters as rotational coordinates.
许多三维刚体动力学模型采用欧拉参数作为旋转坐标。由于四个欧拉参数并非相互独立，因此在运动方程中必须考虑四元数约束。这通常通过拉格朗日乘数法来实现。在本文中，将推导各种形式的旋转运动方程，并证明它们可以相互转换。在此特别关注拉格朗日乘数的值以及表示惯性力的项的复杂性。还特别关注旋转广义外力矢量，当使用欧拉参数作为旋转坐标时，该矢量不是唯一的。
