共查询到20条相似文献，搜索用时 640 毫秒
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《实验室研究与探索》2015,(1):113-117
本文运用求常微方程数值解的四阶龙格-库塔方法,确定了描述单摆运动的非线性微分方程数值解的龙格-库塔公式;用Excel的迭代计算和循环迭代功能确定了数值解,求出单摆在各个时刻的速度和位置;巧用绘制图像和实现动画功能"数"、"形"及"动"连贯形象直观地演示了单摆运动的动态模拟仿真;实现交互性,建立了不同参数情况下研究单摆运动和模拟的平台,得出了单摆无阻尼、有阻尼、摆角为任何角度值时,速度和位置的数值解,速度和位置的曲线和相应的相图;结果显示,Excel在单摆运动分析中的应用,不仅实现数值计算、绘制图像和动画演示,而且弥补实际实验的不足,为物理理论和实验的计算机辅助教学提供了一种简单、直观、高效的方法。 相似文献
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尹芬芬 《教育前沿(综合版)》2014,(10)
单摆一直是物理学中重要的研究内容之一。由于受到各种因素的影响,单摆的实际运动过程非常复杂。比如考虑大摆角、摆线有弹性、有介质阻力、单摆变为偏摆等因素时,单摆的运动情况都会发生变化,描述运动的相关物理量亦会不同。所以本文通过从中学教学的抽象理想模型出发,结合实际的影响因素,从理论上研究理想模型、大摆角、摆线有弹性、有介质阻力、考虑介质密度等不同情况下的单摆运动,通过建立具体的运动微分方程来推导相关公式并得出结果。 相似文献
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《实验室研究与探索》2013,(11):65-68
自由振动的单摆在大角度摆动时,动力学方程是非线性的,非线性系统复杂行为的一种重要研究方法就是数值计算法。通过理论分析,得到无阻尼、有阻尼、及弹簧单摆大角度振动的动力学方程。利用Matlab软件,观察弹簧单摆的振动现象,求出弹簧单摆非线性微分方程的数值解,展现大角度自由振动单摆周期与角振幅的关系曲线、大角度自由振动和阻尼振动的单摆的相轨迹。对不同条件单摆进行数值模拟,从而直观地研究了不同条件单摆的运动。结果表明,Matlab软件在振动问题中的应用,不仅实现了数值计算高效快捷、绘制图像形象直观,而且弥补了实验的不足,为计算机辅助物理教学提供了一个较好的软件。 相似文献
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对于两个具有任意非零色散系数的弱耦合Korteweg-deVries（KdV）方程,得到一类微扰孤子解及其存在性条件．数值结果表明,弱耦合相互作用仅给未扰孤子对以小的修正,不改变孤子的特性． 相似文献
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对于两个具有任意非零色散系数的弱耦合Ｋｏｒｔｅｗｅｇ－ｄｅＶｒｉｅｓ（ＫｄＶ）方程，得到一类微扰孤子解及其存在性条件，数值结果表明，弱耦合相互作用仅给未扰孤子对以小的修正，不改变孤子的特性。 相似文献
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用微扰法和数值法求解了色散缓变光纤中含高阶色散的非线性Schrodinger方程．从理论上分析了光孤子的传输特性．解析解与数值结果符合甚好。 相似文献
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直接从单摆的运动微分方程出发,应用Matlab软件,求出了线性单摆阻尼振动的解析解和非线性单摆无阻尼振动、阻尼振动的数值解;画出了单摆的振动曲线和相图. 相似文献
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方见树 《株洲师范高等专科学校学报》1999,(3)
本文用经典方法求出了E－M（Earth－Moon）系统受扰动时的微扰解,并利用Lyapunov稳定性定理对其微扰解的稳定性问题进行了分析,得到了E－M系统的微扰解是Lyspunov稳定的结论。 相似文献
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When we refer to scientific knowledge, we, implicitly or explicitly, refer to its three components, namely its conceptual framework, its methodological principles and its cultural aspects. The pendulum is a topic of science teaching and learning where all three of these aspects can be examined with the aim of gaining a holistic appreciation of the transformation of a natural phenomenon into a phenomenon of the physical sciences and how this can then be recontextualized into a topic of school science learning. The main objective of this study is to examine whether this richness of the pendulum as a topic of teaching is revealed in the school science textbooks in Greece and Cyprus, for both primary and secondary education. We will use an analytical mapping instrument in order to determine, whether the pendulum is introduced at some grade level and, if so, in what context. We will then use an interpretive instrument, which relies on taxonomy of science curricula into traditional, innovative and constructivist programs, in order to attach meaning to the analysis. Finally, we will formulate a series of proposals in relation to the educational value of the simple pendulum at the Greek and Cypriot gymnasium level. 相似文献
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赵小明 《洛阳工业高等专科学校学报》2005,15(2):35-36,64
采用二维谐振子模型，尝试对侧向扰动下单摆的进动现象进行分析解释，得出线性近似下摆球轨迹的极坐标公式，并对极限情况加以讨论，将单摆、圆锥摆及类椭圆摆动统一起来。进一步定性分析进动是由回复力高次项作用产生的非线性运动，从而使实验现象得到较完整的解释。 相似文献
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C. Medina 《Science & Education》2004,13(7):631-640
This paper conveys information about a Physicslaboratory experiment for students with some theoretical knowledge about oscillatory motion. Students construct a simple pendulum that behaves as an ideal one, and analyze model assumption incidence on its period. The following aspects are quantitatively analyzed: vanishing friction, small amplitude, not extensible string, point mass of the body, and vanishing mass of the string.It is concluded that model assumptions are easilyaccomplished in practice, within small experimental errors. Furthermore, this way of carrying out the usual pendulum experiments promotes a better understanding of the scientific modeling process. It allows a deeper comprehension of those physical concepts associated with model assumptions (small amplitude, point mass, etc.), whose physical and epistemological meanings appear clearly related to the model context. Students are introduced to a scientific way of controlling the validity of theoretical development, and they learn to value the power and applicability of scientific modeling. 相似文献
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C. Medina 《Science & Education》2004,13(7-8):631-640
This paper conveys information about a Physicslaboratory experiment for students with some theoretical knowledge about oscillatory motion. Students construct a simple pendulum that behaves as an ideal one, and analyze model assumption incidence on its period. The following aspects are quantitatively analyzed: vanishing friction, small amplitude, not extensible string, point mass of the body, and vanishing mass of the string. It is concluded that model assumptions are easilyaccomplished in practice, within small experimental errors. Furthermore, this way of carrying out the usual pendulum experiments promotes a better understanding of the scientific modeling process. It allows a deeper comprehension of those physical concepts associated with model assumptions (small amplitude, point mass, etc.), whose physical and epistemological meanings appear clearly related to the model context. Students are introduced to a scientific way of controlling the validity of theoretical development, and they learn to value the power and applicability of scientific modeling. 相似文献
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A unit of study for gifted 4th and 5th graders is described on the subject of mathematical periodicity and chaos and the underlying physical processes which produce these phenomena. A variety of hands-on experiments and the use of various data analysis tools and computer aids provide students with powerful raw material for their analysis, interpretation, and understanding. The concepts of simple periodic motion (e.g., a pendulum), complex superposition of motions (e.g., the vibrations in musical instruments), and chaotic sequences (e.g., stock prices) are covered, with numerous practical examples. Opportunities to involve related activities emphasizing language arts, history, and graphic art are included. The student response to the material is documented. 相似文献
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何松林 《实验室研究与探索》2011,30(6)
由摆球浸入不同温度纯水中的小角阻尼振动实验,发现角振幅衰减及振动周期不随液体黏度发生改变。采用改进平均法求解平方阻尼作用下单摆小角振动微分方程,得到角位移随时间变化的解析表达式,据此得到的角振幅衰减及振动周期的定量结果与实验数据符合。得出结论:摆球在液体中振动时受到的流体阻力是与液体黏度无关的平方阻力;平方阻尼常量与液体的密度成正比,与摆球半径及密度的乘积成反比;摆球浸入液体时的阻尼振动、角振幅衰减是非指数型的,衰减速度和振动周期都与平方阻尼常量密切相关。 相似文献
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Piaget's investigations into children's understanding of the laws governing the movement of a simple pendulum were first reported in 1955 as part of a report into how children's knowledge of the physical world changes during development. Chapter 4 of Inhelder & Piaget (1955/1958) entitled `The Oscillation of a Pendulum and the Operations of Exclusion' demonstrated how adolescents could construct the experimental strategies necessary to isolate each of the variables, exclude the irrelevant factors and conclude concerning the causal role of length. This became one of the most easily replicable tasks from the Genevan school and was used in a number of important investigations to detect the onset of formal operational thinking. While it seems that the pendulum investigation fits nicely into Piaget's sequence of studies of concepts such as time, distance and speed suggested to him by Einstein, more recent research (Bond 2001) shows Inhelder to be directly responsible for the investigations into children's induction of physical laws. The inter-relationship between the pendulum problem, developing thought and scientific method is revealed in a number of Genevan and post-Piagetian investigations. 相似文献
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张卫平 《佳木斯教育学院学报》2012,(9):168-169
此篇通过高等数学相关数学原理结合物理回复力和简谐运动周期公式相关原理推导出单摆的简谐运动周期公式,能比较清楚的了解该公式的推导过程,加强对单摆做简谐运动周期公式的理解。 相似文献