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Time-Varying Square Root Finding
Published in Yunong Zhang, Xiao Lin, Zhengli Xiao, Mingzhi Mao, Zeroing Dynamics, Gradient Dynamics, and Newton Iterations, 2018
Yunong Zhang, Xiao Lin, Zhengli Xiao, Mingzhi Mao
In this simulation example, the four-link robot arm’s end-effector is expected to move along a desired isosceles-right-triangle path with the right-angle side length being 0.8m. The motion duration is 30s, and the initial joint state is θ(0)=[3π/4,-π/2,-π/4,π/6]T rad. Parameters ζ and γ are set to be 4 and 105, respectively. The simulation results are depicted correspondingly in Figure 14.1, Table 14.1, Figures 14.2 and 14.3 as well as Table 14.2.
Impact resistance of concrete pavement surface reinforced with fibre mesh
Published in International Journal of Pavement Engineering, 2023
Jun Zhang, Wei Xu, Xingzhong Weng, Peiwei Gao, Zhihua Yao, Lihai Su, Jiang Wang, Lei Tang, Mingzhe Zhao
Under the sustained action of impact load, a new main crack extending to the slab edge along the perpendicular direction is generated. It then continues to extend downward after intersecting with the slab edge. Afterward, the first principal crack intersects the third principal crack, forming a closed fracture area, which presents a ‘semi-pyramid shape.’ Under the continued impact load, the slab edge left side falls. The second principal crack also rapidly develops, forming a ‘semi-pyramid’ closed area with the third main crack. Finally, the slab edge right side also fails. The gap on the impact failure surface of the slab side is a triangle with an opening and closing angle of 120°, and the gap on the slab edge is an isosceles right triangle. The damage areas at different positions are different in size, and the positions in the order of degree of damage are the slab edge quartile < slab edge trisection < slab edge midpoint.
An associated result of the Van Aubel configuration and its generalization
Published in International Journal of Mathematical Education in Science and Technology, 2023
From the aforementioned, it further follows that if ∠BPA = 90° and ∠PAB = 45°, then PR = QS and PR ⊥ QS. Since this condition implies that △BPA becomes an isosceles right triangle,4 it immediately follows from the similarity of △BPA to △GIF, that the kite GHFI becomes a square.