通过结式和计算机代数研究布里卡德连杆机构及其他结构的灵活性。
Flexibility of Bricard's linkages and other structures via resultants and computer algebra.
作者信息
Lewis Robert H, Coutsias Evangelos A
机构信息
Fordham University, New York, NY 10458, USA.
Stony Brook University, Stony Brook, NY 11794, USA.
出版信息
Math Comput Simul. 2016 Jul;125:152-167. doi: 10.1016/j.matcom.2014.11.002. Epub 2014 Nov 18.
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.
结构的灵活性对于化学和机器人技术极为重要。继我们之前的工作之后，我们使用多项式方程、结式以及我们创建的一种分析结式的符号算法来研究灵活性。我们表明，该软件解决了由布里卡德提出的平面四边形的经典排列问题。我们填补了布里卡德工作中的几个空白，并发现了一些他显然未意识到的新的灵活排列。这为该软件的成熟性提供了有力证据，并且是通过计算机辅助实验进行数学发现的一个绝佳示例。
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