可倒摆方程

７０年代以前，国际上常用可倒摆来测定重力加速度ｇ，虽获巨大成功，但因缺乏更深层次的理论指导而使测量带有盲目性．将该测量移植到大学物理实验中后，此缺陷仍然存在，常使学生困惑．本文导出的可倒摆方程弥补了这一缺陷，也有利于教学．     

单摆衍变类型的剖析

单摆作为中学物理中一个重要的理想化模型，是考试的热点，纵观考查有关单摆的问题几乎可以归纳为一个问题——单摆衍变．下面就对这一问题进行剖析。     

磁通最大原理

用演绎法导出“磁通最大原理”并给出数学表达和应用举例。     

拳击后手摆拳下肢快速发力对出拳速度的影响

运用2块测力台和三维红外高速摄像系统进行同步测试,采集16名优秀男子拳击运动员在后手摆拳全力击打固定目标过程中,双脚地面支撑反作用力及运动学相关数据.双脚快速力量参数与出拳速度进行相关分析、曲线估计,并计算相应的回归方程.结果显示:前、后脚蹬地最大力量/体重、快速力量指数/体质量与出拳速度均呈显著正相关(P＜0.01)；蹬地达到最大力量峰值的时间与出拳速度呈曲线关系(P＜0.01).结论:(1)拳击运动员后手摆拳击打的过程中,双脚积极蹬地发力阶段快速发力对出拳速度均具有显著影响；(2)提高双脚积极蹬地发力阶段蹬地最大力量有助于提高后手摆拳出拳速度；(3)双脚积极蹬地发力阶段,一定范围内,缩短蹬地的发力时间有助于提高出拳速度；(4)提高双脚积极蹬地发力阶段发力速度有助于提高后手摆拳出拳速度；(5)后手摆拳下肢快速发力对出拳速度的影响,同肢体快速发力对自身动作速度的影响显示出趋于一致的规律.     

三线摆周期的旋转矢量求法

由能量方程出发，引入新变量，用旋转矢量法讨论了三线摆大角度摆动时的周期。     

轴向数控磁力轴承系统的研究

本文建立了轴向磁力轴承的动力学方程和数学模型 ,阐述了基于数学模型分析的数字控制系统的设计方法 .介绍了本课题设计的新型数字控制系统 .试验表明该系统具有较好的控制稳定性和运转稳定性 ,具有较强的承载力 .     

三维Minkowski空间中基于Killing向量场的磁力曲线

本文在三维Minkowski空间中,研究了基于Killing向量场的磁力曲线.首先给出了三维Minkowski空间中对应于平移和旋转的所有Killing向量场,并对不同的Killing向量所对应的磁力曲线进行了分类,最后给出了一些磁力曲线的图像.     

Complex dynamics in physical pendulum equation with suspension axis vibrations

The physical pendulum equation with suspension axis vibrations is investigated. By using Melnikov＇s method, we prove the conditions for the existence of chaos under periodic perturbations. By using second-order averaging method and Melinikov＇s method, we give the conditions for the existence of chaos in an averaged system under quasi-periodic perturbations for Ω = nω ＋ εv, n = 1 - 4, where ν is not rational to ω. We are not able to prove the existence of chaos for n = 5 - 15, but show the chaotic behavior for n = 5 by numerical simulation. By numerical simulation we check on our theoretical analysis and further exhibit the complex dynamical behavior, including the bifurcation and reverse bifurcation from period-one to period-two orbits; the onset of chaos, the entire chaotic region without periodic windows, chaotic regions with complex periodic windows or with complex quasi-periodic windows; chaotic behaviors suddenly disappearing, or converting to period-one orbit which means that the system can be stabilized to periodic motion by adjusting bifurcation parameters α, δ, f0 and Ω; and the onset of invariant torus or quasi-periodic behaviors, the entire invariant torus region or quasi-periodic region without periodic window, quasi-periodic behaviors or invariant torus behaviors suddenly disappearing or converting to periodic orbit; and the jumping behaviors which including from period- one orbit to anther period-one orbit, from quasi-periodic set to another quasi-periodic set; and the interleaving occurrence of chaotic behaviors and invariant torus behaviors or quasi-periodic behaviors; and the interior crisis; and the symmetry breaking of period-one orbit; and the different nice chaotic attractors. However, we haven＇t find the cascades of period-doubling bifurcations under the quasi-periodic perturbations and show the differences of dynamical behaviors and technics of research between the periodic perturbations and quasi-periodic perturbations.     

Bifurcations of resonant solutions and chaos in physical pendulum equation with suspension axis vibrations

This paper is a continuation of ＂Complex Dynamics in Physical Pendulum Equation with Suspension Axis Vibrations＂[1].In this paper,we investigate the existence and the bifurcations of resonant solution for ω0：ω：Ω ≈ 1：1：n,1：2：n,1：3：n,2：1：n and 3：1：n by using second-order averaging method,give a criterion for the existence of resonant solution for ω0：ω：Ω ≈ 1：m：n by using Melnikov＇s method and verify the theoretical analysis by numerical simulations.By numerical simulation,we expose some other interesting dynamical behaviors including the entire invariant torus region,the cascade of invariant torus behaviors,the entire chaos region without periodic windows,chaotic region with complex periodic windows,the entire period-one orbits region;the jumping behaviors including invariant torus behaviors converting to period-one orbits,from chaos to invariant torus behaviors or from invariant torus behaviors to chaos,from period-one to chaos,from invariant torus behaviors to another invariant torus behaviors;the interior crisis;and the different nice invariant torus attractors and chaotic attractors.The numerical results show the difference of dynamical behaviors for the physical pendulum equation with suspension axis vibrations between the cases under the three frequencies resonant condition and under the periodic/quasi-periodic perturbations.It exhibits many invariant torus behaviors under the resonant conditions.We find a lot of chaotic behaviors which are different from those under the periodic/quasi-periodic perturbations.However,we did not find the cascades of period-doubling bifurcation.     

The Sumcient and Necessary Condition of Lagrange Stability of Quasi-periodic Pendulum Type Equations

The quasi-periodic pendulum type equations are considered. A sufficient and necessary condition of Lagrange stability for this kind of equations is obtained. The result obtained answers a problem proposed by Moser under the quasi-periodic case.