论文标题
多项式运动接受线性因子的分解
Motion Polynomials Admitting a Factorization with Linear Factors
论文作者
论文摘要
运动多项式（与非零实际规范的双重四聚体上的多项式）描述了理性运动。我们提出了减少有界运动多项式的必要条件，以将因素化为一元线性因子，并给出一种计算它们的算法。我们可以使用这些线性因子来构建机制，因为分数对应于合理运动分解为简单旋转或翻译。有界的运动多项式始终在乘以合适的实际或四元素多项式后，将分解成线性因子。我们的因值化标准使我们能够改善早期算法，以计算合适的实际或四元素多项式辅助因素。
Motion polynomials (polynomials over the dual quaternions with nonzero real norm) describe rational motions. We present a necessary and sufficient condition for reduced bounded motion polynomials to admit factorizations into monic linear factors, and we give an algorithm to compute them. We can use those linear factors to construct mechanisms because the factorization corresponds to the decomposition of the rational motion into simple rotations or translations. Bounded motion polynomials always admit a factorization into linear factors after multiplying with a suitable real or quaternion polynomial. Our criterion for factorizability allows us to improve on earlier algorithms to compute a suitable real or quaternion polynomial co-factor.
