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直线轨迹定理与直线机构及其演化
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作者 张清珍 《现代机械》 北大核心 1992年第3期26-28,共3页
对直线轨迹几何定理作了证明,据此给出了六杆和八杆两种精确的直线运动机构,并对波斯里八杆直线运动机构的演化进行了讨论和例证,使其应用直线轨迹定理创造新的直线运动机构和应用所述的两种直线运动机构更加自觉。
关键词 直线轨迹定理 直线机构 演化
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一个二次曲线平行弦中点的轨迹定理及应用
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作者 张赞源 《中学教研(数学版)》 1990年第4期13-15,共3页
一阶导数与二次曲线弦中点间存在着一种内在联系,这种联系为解决二次曲线中点弦一类问题开辟了一条较为简捷的路径.本文就以定理形式揭示这种联系并列举应用. 定理:椭圆x<sup>2</sup>/a<sup>2</sup>+y<sup&g... 一阶导数与二次曲线弦中点间存在着一种内在联系,这种联系为解决二次曲线中点弦一类问题开辟了一条较为简捷的路径.本文就以定理形式揭示这种联系并列举应用. 定理:椭圆x<sup>2</sup>/a<sup>2</sup>+y<sup>2</sup>/b<sup>2</sup>=1的以斜率为k的一组平行弦中点轨迹方程是x<sup>2</sup>/a<sup>2</sup>+yy<sub>x</sub><sup>’</sup>/b<sup>2</sup>=0(※)(|x|≤a,|y|≤b)其中y<sub>x</sub><sup>’</sup>就是平行弦的斜率k,它等于直线(※)与椭圆交点处切线的斜率. 证明:设点P(x<sub>0</sub>,y<sub>0</sub>)是以k为斜率的弦P<sub>1</sub>P<sub>2</sub>的中点,点P<sub>1</sub>(x<sub>1</sub>,y<sub>1</sub>),P<sub>2</sub>(x<sub>2</sub>,y<sub>2</sub>) 展开更多
关键词 二次曲线 中点弦 轨迹方程 轨迹定理 椭圆型 抛物线方程 曲线方程 一阶导数 题设条件 点坐标
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基于NFTET的高超声速飞行器鲁棒轨迹重构设计 被引量:2
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作者 郭小平 齐瑞云 《南京航空航天大学学报》 EI CAS CSCD 北大核心 2017年第S1期82-88,共7页
考虑高超声速飞行器故障下安全再入飞行问题,针对飞行器发生较大故障的情况,提出了基于相邻可行轨迹存在定理(Neighboring feasible trajectory existence theorem,NFTET)的鲁棒在线轨迹重构算法。在标称情况下基于反馈线性化预测校正... 考虑高超声速飞行器故障下安全再入飞行问题,针对飞行器发生较大故障的情况,提出了基于相邻可行轨迹存在定理(Neighboring feasible trajectory existence theorem,NFTET)的鲁棒在线轨迹重构算法。在标称情况下基于反馈线性化预测校正制导算法生成满足各种约束条件的再入轨迹;由于NFTET只适用于发生较小故障的情况,为保证较大故障下飞行器仍能以较高精度安全着陆,基于NFTET理论设计了鲁棒轨迹重构算法,得到了较高落点精度的飞行轨迹。仿真结果表明,本文所提出算法能有效解决飞行器较大故障下的安全再入轨迹重构问题,提高了飞行器的自主容错能力。 展开更多
关键词 高超声速飞行器 安全再入 相邻可行轨迹存在定理 鲁棒轨迹重构算法 自主容错
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例析以“阿波罗尼斯圆”为背景的热点考向
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作者 付峰峰 《中学生数理化(高二数学、高考数学)》 2023年第20期20-23,共4页
古希腊著名数学家阿波罗尼斯发现:在平面上给定两点A,B,设P点在同一平面上且满足|PA|/|PB|=λ,当λ>0且λ≠1时,P点的轨迹是个圆,称之为阿波罗尼斯圆,又称阿氏圆。当λ=1时,P点的轨迹是线段AB的中垂线,这个结论称作阿波罗尼斯轨迹定理。
关键词 阿波罗尼斯圆 著名数学家 中垂线 轨迹定理 阿氏圆 例析
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高考部分数学试题简捷解法
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作者 一木 《数学教学通讯》 1982年第3期41-45,共5页
1978年到1980年全国高考数学试题,教育部发下的命题小组所写的解答,绝大多数都是很好的,既提供评卷老师参考,也有利于中学数学教学。但是,有少数题的解法虽然有三、四个,但却没有一个较简捷的解法。当然有些数学题的解法往往不止一个,... 1978年到1980年全国高考数学试题,教育部发下的命题小组所写的解答,绝大多数都是很好的,既提供评卷老师参考,也有利于中学数学教学。但是,有少数题的解法虽然有三、四个,但却没有一个较简捷的解法。当然有些数学题的解法往往不止一个,命题小组不可能提出全部解法。 展开更多
关键词 高考数学 中学数学教学 换底公式 证法 轨迹方程 轨迹定理 正弦定理 当且仅当 教学参考 参数方程
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从一道大赛题谈起
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作者 盛焕远 《中学数学教学》 1993年第5期35-36,共2页
1992年全国初中联赛二试几何题的内涵相当丰富。我在寻找此题的逆命题时,发现了一些有趣的事情,写出来供参考。 1.为叙述方便,先写出n个条件(图1)。(A)等腰条件:AB=AC;(B)三分条件;BD= 2DC;(C)倍长条件:BE= 2EA;(D)等角条件:∠BED=∠BAC... 1992年全国初中联赛二试几何题的内涵相当丰富。我在寻找此题的逆命题时,发现了一些有趣的事情,写出来供参考。 1.为叙述方便,先写出n个条件(图1)。(A)等腰条件:AB=AC;(B)三分条件;BD= 2DC;(C)倍长条件:BE= 2EA;(D)等角条件:∠BED=∠BAC;(E)倍角条件:∠BED=2∠DEC。在本文中,条件(C)十分重要。 展开更多
关键词 等角条件 四点共圆 外分点 中学数学教学 两圆相切 公共点 轨迹定理 勾股 分角线 知原
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Consensus and formation control of discrete-time multi-agent systems 被引量:6
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作者 王婧 年晓红 王海波 《Journal of Central South University》 SCIE EI CAS 2011年第4期1161-1168,共8页
Consensus problems for discrete-time multi-agent systems were focused on. In order to design effective consensus protocols, which were aimed at ensuring that the concerned states of agents converged to a common value,... Consensus problems for discrete-time multi-agent systems were focused on. In order to design effective consensus protocols, which were aimed at ensuring that the concerned states of agents converged to a common value, a new consensus protocol for general discrete-time multi-agent system was proposed based on Lyapunov stability theory. For discrete-time multi-agent systems with desired trajectory, trajectory tracking and formation control problems were studied. The main idea of trajectory tracking problems was to design trajectory controller such that each agent tracked desired trajectory. For a type of formation problem with fixed formation structure, the formation structure set was introduced. According to the formation structure set, each agent can track its individual desired trajectory. Finally, simulations were provided to demonstrate the effectiveness of the theoretical results. The mlmerical results show that the states of agents converge to zero with consensus protocol, which is said to achieve a consensus asymptotically. In addition, through designing appropriate trajectory controllers, the simulation results show that agents converge to the desired trajectory asymptotically and can form different formations. 展开更多
关键词 multi-agent system CONSENSUS trajectory tracking FORMATION
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Trajectory tracking and formation control based on consensus in high-dimensional multi-agent systems 被引量:1
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作者 Su Saijun Nian Xiaohong Pan Huan 《High Technology Letters》 EI CAS 2012年第3期326-332,共7页
This paper discusses consensus problems for high-dimensional networked multi-agent systems with fixed topology. The communication topology of multi-agent systems is represented by a digraph. A new consensus protocol i... This paper discusses consensus problems for high-dimensional networked multi-agent systems with fixed topology. The communication topology of multi-agent systems is represented by a digraph. A new consensus protocol is proposed, and consensus convergence of multigent systems is analyzed based on the Lyapunov stability theory. The consensus problem can be formulated into solving a feasible problem with bilinear matrix inequality (BMI) constrains. Furthermore, the consensus protocol is extended to achieving tracking and formation control. By introducing the formation structure set, each agent can gain its individual desired trajectory. Finally, numerical simulations are provided to show the effectiveness of our strategies. The results show that agents from arbitrary initial states can asymptotically reach a consensus. In addition, agents with high-dimensional can track any target trajectory, and maintain desired formation during movement by selecting appropriate structure set. 展开更多
关键词 consensus protocol multi-agent systems fixed topology trajectory tracking for-mation control
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基于NFTET的高超声速飞行器再入容错制导 被引量:3
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作者 钱佳淞 齐瑞云 《航空学报》 EI CAS CSCD 北大核心 2015年第10期3370-3381,共12页
针对以X-33为对象的三自由度高超声速飞行器,采用相邻可行轨迹存在定理(NFTET)设计了容错制导律以解决再入段执行器发生故障的轨迹重构问题。在标称情况下采用预测校正算法生成满足再入过程约束和终端约束要求的再入轨迹;当执行器发生... 针对以X-33为对象的三自由度高超声速飞行器,采用相邻可行轨迹存在定理(NFTET)设计了容错制导律以解决再入段执行器发生故障的轨迹重构问题。在标称情况下采用预测校正算法生成满足再入过程约束和终端约束要求的再入轨迹;当执行器发生故障时,飞行器气动参数、结构和舵面力矩都可能发生不可预测的变化,原先的轨迹不再满足制导要求,因此需要设计新型容错制导律。针对实际再入制导模型,基于NFTET设计容错制导算法对轨迹进行重构,得到满足故障情况下制导任务的可行轨迹。从仿真结果中可以看出,容错制导算法生成的新轨迹重新回到了约束范围之内,轨迹呈收敛趋势,使得高超声速飞行器从故障恢复到正常飞行状态,提高了飞行器的自主容错能力。 展开更多
关键词 高超声速飞行器 预测校正制导 容错制导 重构轨迹 相邻可行轨迹存在定理(NFTET)
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TRAJECTORY TRACKING THEORY OF QUANTUM SYSTEMS 被引量:3
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作者 CONG Shuang LIU Jianxiu 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2014年第4期679-693,共15页
The orbit tracking problem of a free-evolutionary target system in closed quantum systems is solved by changing it into the state transferring problem with the help of unitary transformation.The control law designed b... The orbit tracking problem of a free-evolutionary target system in closed quantum systems is solved by changing it into the state transferring problem with the help of unitary transformation.The control law designed by the Lyapunov stability theorem employs a carefully constructed virtual mechanical quantity P to ensure the system convergence.The virtual mechanical quantity P is chosen by two approaches according to the forms of limit set,where P = —pf is suitable for regular limit set and a new different P is constructed for irregular one.The proposed tracking control theory is demonstrated on a four-level quantum system by means of numerical simulation experiments. 展开更多
关键词 CONVERGENCE limit set Lyapunov stability theorem orbit tracking.
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