The purpose of the present work is to derive some solutions for several solid angle cases via a fundamental formula which gives the solid angle for an isosceles triangle. From this formula the solid angle of pyramids ...The purpose of the present work is to derive some solutions for several solid angle cases via a fundamental formula which gives the solid angle for an isosceles triangle. From this formula the solid angle of pyramids is derived but, unlike other presentations, it is shown in a format similar to that of the well-known cone case. Besides the regular polygon cases (straight pyramids), solid angles of some other plane closed curves are calculated. The fundamental formula also leads to some interesting properties showing the not simple behavior of solid angles with the observer point on the curve itself, as it depends on how the observer arrived there. The question of the equi-Ω surfaces is also discussed and calculated in simple cases.展开更多
Large torque can be output by the single gimbal control momentum gyroscope (SGCMG) based on the principle of the gyroscopic precession. However, the singularity is a major obstacle to successfully implement the task o...Large torque can be output by the single gimbal control momentum gyroscope (SGCMG) based on the principle of the gyroscopic precession. However, the singularity is a major obstacle to successfully implement the task of the attitude control. The singularity can be avoided by the additional variable flywheel speed of variable speed control moment gyroscopes (VSCMG). Unfortunately, some kind of singularity cannot be effectively avoided. Consequently, the output toque can be only supported by the reaction torque of the flywheel when the singularity is encountered, and the consume power that is determined by the flywheel speed and reaction torque can be greatly increased when the flywheel spin rate over one thousand revolutions per minute. In this paper, the pyramid configuration with variable skew angle of the VSCMG is considered. A new steering law for the VSCMG with variable skew angle is proposed. The singularity that cannot be avoided by the varying flywheel speed can be effectively avoided with assisting of varying the skew angle. Consequently, the requirement of flywheel torque can be reduced. At last, the optimizing VSCMG with variable skew angle can be cast as a multi-objective function with multi-constraints. The particle swarm optimization method is used to solve the optimizing problem. In summary, the VSCMG with variable skew angle can be redesigned with considering of the singularity avoidance and minimizing system power.展开更多
The simulation of indentations with so called “equivalent” pseudo-cones for decreasing computer time is challenged. The mimicry of pseudo-cones having equal basal surface and depth with pyramidal indenters is exclud...The simulation of indentations with so called “equivalent” pseudo-cones for decreasing computer time is challenged. The mimicry of pseudo-cones having equal basal surface and depth with pyramidal indenters is excluded by basic arithmetic and trigonometric calculations. The commonly accepted angles of so called “equivalent” pseudo-cones must not also claim equal depth. Such bias (answers put into the questions to be solved) in the historical values of the generally used half-opening angles of pseudo-cones is revealed. It falsifies all simulations or conclusions on that basis. The enormous errors in the resulting hardness H<sub>ISO</sub> and elastic modulus E<sub>r-ISO</sub> values are disastrous not only for the artificial intelligence. The straightforward deduction for possibly ψ-cones (ψ for pseudo) without biased depths’ errors for equal basal surface and equal volume is reported. These ψ-cones would of course penetrate much more deeply than the three-sided Berkovich and cube corner pyramids (r a/2), and their half-opening angles would be smaller than those of the respective pyramids (reverse with r > a/2 for four-sided Vickers). Also the unlike forces’ direction angles are reported for the more sideward and the resulting downward directions. They are reflected by the diameter of the parallelograms with length and off-angle from the vertical axis. Experimental loading curves before and after the phase-transition onsets are indispensable. Mimicry of ψ-cones and pyramids is also quantitatively excluded. All simulations on their bases would also be dangerously invalid for industrial and solid pharmaceutical materials.展开更多
为提高拍摄颞骨岩部 X 线轴位与斜位片的影像质量,对130个成人整颅颅指数与锥体角的关系进行观察研究,见130例260侧锥体角全在48°以上,平均57°;计算颅指数与锥体角间的相关系数并推算根据颅指数估计锥体角的回归方程,见锥体...为提高拍摄颞骨岩部 X 线轴位与斜位片的影像质量,对130个成人整颅颅指数与锥体角的关系进行观察研究,见130例260侧锥体角全在48°以上,平均57°;计算颅指数与锥体角间的相关系数并推算根据颅指数估计锥体角的回归方程,见锥体角与颅指数高度相关,二者之间具有直线回归关系。故作者认为拍摄骨岩部轴位片与斜位片时头部偏转角不应固定为45°,该角大小应取决于锥体角。可通过对病人头长头宽的测量得知头指数而确定锥体角的估计值,按此估计值拍片可提高岩锥摄片质量。展开更多
文摘The purpose of the present work is to derive some solutions for several solid angle cases via a fundamental formula which gives the solid angle for an isosceles triangle. From this formula the solid angle of pyramids is derived but, unlike other presentations, it is shown in a format similar to that of the well-known cone case. Besides the regular polygon cases (straight pyramids), solid angles of some other plane closed curves are calculated. The fundamental formula also leads to some interesting properties showing the not simple behavior of solid angles with the observer point on the curve itself, as it depends on how the observer arrived there. The question of the equi-Ω surfaces is also discussed and calculated in simple cases.
文摘Large torque can be output by the single gimbal control momentum gyroscope (SGCMG) based on the principle of the gyroscopic precession. However, the singularity is a major obstacle to successfully implement the task of the attitude control. The singularity can be avoided by the additional variable flywheel speed of variable speed control moment gyroscopes (VSCMG). Unfortunately, some kind of singularity cannot be effectively avoided. Consequently, the output toque can be only supported by the reaction torque of the flywheel when the singularity is encountered, and the consume power that is determined by the flywheel speed and reaction torque can be greatly increased when the flywheel spin rate over one thousand revolutions per minute. In this paper, the pyramid configuration with variable skew angle of the VSCMG is considered. A new steering law for the VSCMG with variable skew angle is proposed. The singularity that cannot be avoided by the varying flywheel speed can be effectively avoided with assisting of varying the skew angle. Consequently, the requirement of flywheel torque can be reduced. At last, the optimizing VSCMG with variable skew angle can be cast as a multi-objective function with multi-constraints. The particle swarm optimization method is used to solve the optimizing problem. In summary, the VSCMG with variable skew angle can be redesigned with considering of the singularity avoidance and minimizing system power.
文摘The simulation of indentations with so called “equivalent” pseudo-cones for decreasing computer time is challenged. The mimicry of pseudo-cones having equal basal surface and depth with pyramidal indenters is excluded by basic arithmetic and trigonometric calculations. The commonly accepted angles of so called “equivalent” pseudo-cones must not also claim equal depth. Such bias (answers put into the questions to be solved) in the historical values of the generally used half-opening angles of pseudo-cones is revealed. It falsifies all simulations or conclusions on that basis. The enormous errors in the resulting hardness H<sub>ISO</sub> and elastic modulus E<sub>r-ISO</sub> values are disastrous not only for the artificial intelligence. The straightforward deduction for possibly ψ-cones (ψ for pseudo) without biased depths’ errors for equal basal surface and equal volume is reported. These ψ-cones would of course penetrate much more deeply than the three-sided Berkovich and cube corner pyramids (r a/2), and their half-opening angles would be smaller than those of the respective pyramids (reverse with r > a/2 for four-sided Vickers). Also the unlike forces’ direction angles are reported for the more sideward and the resulting downward directions. They are reflected by the diameter of the parallelograms with length and off-angle from the vertical axis. Experimental loading curves before and after the phase-transition onsets are indispensable. Mimicry of ψ-cones and pyramids is also quantitatively excluded. All simulations on their bases would also be dangerously invalid for industrial and solid pharmaceutical materials.
文摘为提高拍摄颞骨岩部 X 线轴位与斜位片的影像质量,对130个成人整颅颅指数与锥体角的关系进行观察研究,见130例260侧锥体角全在48°以上,平均57°;计算颅指数与锥体角间的相关系数并推算根据颅指数估计锥体角的回归方程,见锥体角与颅指数高度相关,二者之间具有直线回归关系。故作者认为拍摄骨岩部轴位片与斜位片时头部偏转角不应固定为45°,该角大小应取决于锥体角。可通过对病人头长头宽的测量得知头指数而确定锥体角的估计值,按此估计值拍片可提高岩锥摄片质量。
