Flexibility of Bricard's linkages and other structures via resultants and computer algebra.
Flexibility of Bricard's linkages and other structures via resultants and computer algebra.
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Bricard 连接和其他结构通过结果和计算机代数的灵活性。
DOI：
10.1016/j.matcom.2014.11.002
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发表时间：
2016
影响因子：
4.6
通讯作者：
Coutsias,EvangelosA
中科院分区：
文献类型：
--
作者：
Lewis,RobertH;Coutsias,EvangelosA
结构的灵活性对化学和机器人技术非常重要。在我们早期的工作之后，我们使用多项式方程，结果和我们创建的分析结果的符号算法来研究灵活性。我们表明，该软件解决了一个经典的安排，四边形在平面上，由于Bricard。我们填补了Bricard工作中的几个空白，发现了他显然不知道的新的灵活安排。这为软件的成熟提供了强有力的证据，也是通过计算机辅助实验进行数学发现的一个很好的例子。
Flexibility of structures is extremely important for chemistry and robotics. Following our earlier work, we study flexibility using polynomial equations, resultants, and a symbolic algorithm of our creation that analyzes the resultant. We show that the software solves a classic arrangement of quadrilaterals in the plane due to Bricard. We fill in several gaps in Bricard’s work and discover new flexible arrangements that he was apparently unaware of. This provides strong evidence for the maturity of the software, and is a wonderful example of mathematical discovery via computer assisted experiment.