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从方向周数的角度来理解终边相同的角
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作者 邓勇 《数学学习与研究》 2016年第21期130-130,132,共2页
三角函数在教学中是一个重点,“终边相同的角”是三角函数中的重点之一.本文对三角函数中终边相同的角做了一些分析探讨,重点对终边相同的角的集合K的K进行了分析,定义了方向周数和方向整周数,并给出了K的几何意义,最后给出了终边相同... 三角函数在教学中是一个重点,“终边相同的角”是三角函数中的重点之一.本文对三角函数中终边相同的角做了一些分析探讨,重点对终边相同的角的集合K的K进行了分析,定义了方向周数和方向整周数,并给出了K的几何意义,最后给出了终边相同的角的几个应用. 展开更多
关键词 三角函 终边相同的角 旋转 方向整周 方向周数
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An Investigation of Restarted GMRES Method by Using Flexible Starting Vectors
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作者 Qiang Niu Lin-Zhang LU 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE 2010年第3期338-351,共14页
We discuss a variant of restarted GMRES method that allows changes of the restarting vector at each cycle of iterations.The merit of the variant is that previously generated information can be utilized to select a new... We discuss a variant of restarted GMRES method that allows changes of the restarting vector at each cycle of iterations.The merit of the variant is that previously generated information can be utilized to select a new starting vector,such that the occurrence of stagnation be mitigated or the convergence be accelerated.The more appealing utilization of the new method is in conjunction with a harmonic Ritz vector as the starting vector,which is discussed in detail.Numerical experiments are carried out to demonstrate that the proposed procedure can effectively mitigate the occurrence of stagnation due to the presence of small eigenvalues in modulus. 展开更多
关键词 Linear systems of equations Arnoldi process GMRES harmonic Ritz vector.
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A CONTROL ALGORITHM FOR RAPID MOVEMENTS NEAR THE RADIUS COMPENSATION SINGULARITY IN FIVE-AXIS END MILLING
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作者 WANG Feng LIN Hu +3 位作者 ZHENG Liaomo LIU Feng YANG Lei GENG Cong 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2013年第5期718-734,共17页
When the five-axis CNC system executes the 3D cutter radius compensation function,the angle between two adjacent radius compensation vectors might become very large and the linear axes would move too fast if the tool ... When the five-axis CNC system executes the 3D cutter radius compensation function,the angle between two adjacent radius compensation vectors might become very large and the linear axes would move too fast if the tool orientation vector is close to the surface normal.The reason that results in this phenomenon is analyzed based on building the transmission relationship between the cutter contact point and the cutter location point.By taking the square-end tool as an example,an optimization algorithm to control the undesired movements is advanced.For the singular area where sudden change exists,the number of interpolation cycles is determined by the cutter feedrate,the limit speeds of machine axes and the maximum allowable angle between radius compensation vectors of adjacent NC blocks.The radius compensation vector of each interpolation cycle is obtained by a kind of vector rotation method.By maintaining the perpendicularity between the radius compensation vector and the tool orientation vector,the rapid movements of the linear axes are eliminated.A trial-cut experiment is performed to verify the correctness and the effectiveness of the proposed algorithm. 展开更多
关键词 Five-axis machining motion control SINGULARITY 3D radius compensation.
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