Constrained multibody kinematics and dynamics in absolute coordinates: a discussion of three approaches to representing rigid body rotation
Constrained multibody kinematics and dynamics in absolute coordinates: a discussion of three approaches to representing rigid body rotation
复制标题
绝对坐标中的约束多体运动学和动力学：对表示刚体旋转的三种方法的讨论
DOI：
10.1115/1.4055140
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发表时间：
2022
期刊：
影响因子：
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通讯作者：
D. Negrut
中科院分区：
文献类型：
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作者：
Alexandra Kissel;Jay Taves;D. Negrut
我们比较了三种方法构成的指数3微分代数方程组（DAE）与约束多体动力学问题制定在绝对坐标。第一种方法直接与定向矩阵一起工作，因此避免了对用于产生定向矩阵A的广义坐标的需要。这种方法是由旋转矩阵属于SO（3）Lie矩阵群的事实所告知的。第二种方法使用欧拉参数，而第三种方法使用欧拉角。在所有情况下，索引3 DAE问题通过一阶隐式数值积分器来解决。我们注意到rA相对于rε的加速大约是2倍，rε相对于rp的加速大约是1.2 - 1.3倍。这些测试是结合四个3D机制进行的。rA方法的仿真速度的改进可以追溯到更简单的运动方程形式和更简洁的雅可比矩阵，这些雅可比矩阵进入数值解。在此作出的贡献是双重的。首先，我们提供了在隐式积分的上下文中使用时进入rA公式的所有量的一阶变化;即，所有下副关节的运动学约束的灵敏度，以及约束反作用力的灵敏度。其次，据我们所知，在绝对坐标系下提出的多体动力学问题中，没有其他贡献可以比较rA、rp和rε的解效率。
We compare three approaches to posing the index 3 set of differential algebraic equations (DAEs) associated with the constrained multibody dynamics problem formulated in absolute coordinates. The first approach works directly with the orientation matrix and therefore eschews the need for generalized coordinates used to produce the orientation matrix A. The approach is informed by the fact that rotation matrices belong to the SO(3) Lie matrix group. The second approach employs Euler parameters, while the third uses Euler angles. In all cases, the index 3 DAE problem is solved via a first order implicit numerical integrator. We note a roughly twofold speedup of rA over rε, and a 1.2 – 1.3 times speedup of rε over rp. The tests were carried out in conjunction with four 3D mechanisms. The improvements in simulation speed of the rA approach are traced back to a simpler form of the equations of motion and more concise Jacobians that enter the numerical solution. The contributions made herein are twofold. First, we provide first order variations of all the quantities that enter the rA formulation when used in the context of implicit integration; i.e., sensitivity of the kinematic constraints for all lower pair joints, as well as the sensitivity of the constraint reaction forces. Second, to the best of our knowledge, there is no other contribution that compares head to head the solution efficiency of rA, rp, and rε in the context of the multibody dynamics problem posed in absolute coordinates.