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线性微分约束,也称Pfafi约束是工程领域中常见的一种微分约束,其可积性是判断该约束是否为完整约束的准则.许多分析力学教材和研究非完整系统的教材都给出了Pfafi约束可积的充要条件但并未证明.本文给出了Pfafi约束可积的充要条件的简捷证明方法,仅采用高等数学中所授场论部分的基本内容,供分析力学课程教学的教师和学习相关课程的学生参考. 相似文献
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研究带有非完整约束的一类多体系统运动规划问题。多体系统中的非完整约束通常是由不可积的速度约束或不可积的守恒律引起。在系统动量和动量矩守恒情况下,动力学方程降阶为非完整形式约束方程,系统的控制问题可转化为无漂移系统的非完整运动规划问题。文中首先导出具有多体开链系统的非完整运动模型。利用最优控制理论和最优化技术,采用输入参数化的方法将连续的最优控制问题转化为离散的最优控制问题,提出一种非完整多体系统运动规划的拟牛顿算法。最后将该方法用于自由漂浮的空间三连杆机构,仿真结果验证了该方法的有效性。 相似文献
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孔向东 《非线性动力学学报》1998,5(2):126-131
本文从Baumgarte的约束久修正法出发,推出了非生动力学微分/代数混合方程约束韧约的自动修正算法,给出了完整约束柔体系统动力学方程的数值求解方法,数值算例说明了该精度和有效性。 相似文献
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多体系统动力学方程为3阶微分代数方程,已有的约束违约稳定法存在位移违约问题,数值仿真准确性和稳定性不足。本文将求解高阶微分代数方程的降阶理论、ε嵌入处理方式与隐式龙格库塔法相结合,提出了直接满足位移约束条件的多体系统动力学方程的无违约算法,避免了约束违约问题。该方法先将多体动力学方程转化为2阶微分代数方程,并与位移约束方程联立;再应用ε嵌入隐式龙格库塔法进行数值求解。应用两种方法分别对单摆机构进行数值仿真,结果表明本文的方法不仅能适应较大步长,且准确性和稳定性均优于约束违约稳定法。 相似文献
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双面约束多点摩擦多体系统的建模和数值方法 总被引:3,自引:1,他引:2
提出了一种建立具有固定双面约束多点摩擦的多体系统动力学方程的方法. 用笛卡尔坐标阵描述系统的位形,根据局部方法的递推关系建立系统的约束方程,应用第一类Lagrange方程建立该系统的动力学方程,使得具有摩擦的约束面的法向力与Lagrange乘子一一对应,便于摩擦力的分析与计算,并用矩阵形式给出了摩擦力的广义力的一般表达式. 应用增广法将微分-代数方程组转化为常微分方程组,并用分块矩阵的形式给出,以便于方程的编程与计算.给出了一种改进的试算法,可提高计算效率. 最后给出了一个算例,应用试算法和RK法对算例进行了数值仿真. 相似文献
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边缘弹性约束圆薄板的大挠度分析 总被引:1,自引:0,他引:1
本文用微分求积法对边缘受弹性约束的弹性圆薄板进行了大挠度分析,详细研究了不同轴对称载荷情况下,边缘面内约束刚度和转动约束刚度对圆板挠度及应力的影响;给出了完全自由或完全固定边界支持计算模型的条件。所得计算结果结论对于工程设计具有一定的指导意义。 相似文献
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预紧弹性约束对系统主共振的影响 总被引:1,自引:0,他引:1
用平均法研究了含预紧弹性约束的单自由度系统在简谐激励下的主共振及其稳定性。发现预紧使主共振明显复杂化:一是存在四种持久的主共振,其运动与约束一擦边即可能失稳;二是共存的周期运动会从三种增加到五种,其中二种不稳定 相似文献
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IntroductionIn1979,R.BengtssonandS.Franendorfaccuratlymeasuredthemaximumvaluesofthespinvelocityof14kindsofnucleons,andtheresultsshowedthatthemaximumvalueofthespinvelocityofonenucleonwasdifferenttothoseoftheothers[1].Withthedevelopmentofscienceandtechnology,… 相似文献
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On the Noether symmetry and Lie symmetry of mechanical systems 总被引:1,自引:0,他引:1
The Noether symmetry is an invariance of Hamilton action under infinitesimal transformations of time and the coordinates.
The Lie symmetry is an invariance of the differential equations of motion under the transformations. In this paper, the relation
between these two symmetries is proved definitely and firstly for mechanical systems. The results indicate that all the Noether
symmetries are Lie symmetries for Lagrangian systems meanwhile a Noether symmetry is a Lie symmetry for the general holonomic
or nonholonomic systems provided that some conditions hold.
The project supported by the National Natural Science Foundation of China (19972010) 相似文献
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Lie symmetries and conserved quantities of second-order nonholonomic mechanical system 总被引:3,自引:0,他引:3
方建会 《应用数学和力学(英文版)》2002,23(9):1105-1110
The Lie symmetries and the conserved quantities of the second-order nonholonomic mechanical system are studied. Firstly, by using the invariance of the differential equation of motion under the infinitesimal transformations, the determining equations and the restriction equations of the Lie symmetries of the system are established, and the structure equation and the conservative quantities of the Lie symmetries are obtained. Secondly , the inverse problems of the Lie symmetries are studied . Finally , an example is given to illustrate the application of the result. 相似文献
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本文研究质量非完整系统的Lie对称性逆问题:根据已知积分求相应的Lie对称性,具体研究了受Chetaev型和非Chetaev型非完整约束的变质量系统的Lie对称性逆问题。首先,根据Lie对称所满足的确定方程和限制方程,给出Lie对称的结构方程和相应的守恒量及其表达式;其次,由已知守恒量求出相应的Noether对称性;最后,根据Noether对称性求出相应的Lie对称性。 相似文献
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相空间中有二阶线性单面约束的非完整系统的Lie对称性与守恒量 总被引:4,自引:0,他引:4
研究相空间中有二阶线性单面约束的非完整系统的Lie对称性与守恒量。首先根据微分方程在无限小变换下的不变性建立Lie对称性所满足的确定方程和限制方程,给出结构方程和守恒量;其次讨论系统的Lie对称性逆问题。最后举一实例说明结果的应用。 相似文献
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IntroductionThestudyofsymmetryandconservedquantityofmechanicalsystemisanimportanttopicinmathematics,mechanicsandphysics .ThemoderntheoriesofsymmetryandconservedquantityofmechanicalsystemincludeNoethersymmetrytheoryandLiesymmetrytheory .In 1979M .Lutzkyando… 相似文献
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The conformal invariance and conserved quantity for the nonholonomic system of non-Chetaev’s type are studied. Firstly, by
introducing a one-parameter infinitesimal transformation group and its infinitesimal generator vector, the definition of conformal
invariance and determining equation for the holonomic system which corresponds to a nonholonomic system of non-Chetaev’s type
are provided, and the relationship between the system’s conformal invariance and Lie symmetry are discussed. Secondly, the
conformal invariance of weak and strong Lie symmetry for the nonholonomic system of non-Chetaev’s type is given using restriction
equations and additional restriction equations. Thirdly, the system’s corresponding conserved quantity is derived with the
aid of a structure equation that the gauge function satisfies. Lastly, an example is given to illustrate the application of
the method and its result. 相似文献
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For a weakly nonholonomic system, the Lie symmetry and approximate Hojman conserved quantity of Appell equations are studied. Based on the Appell equations for a weakly nonholonomic system under special infinitesimal transformations of a group in which the time is invariable, the definition of the Lie symmetry of the weakly nonholonomic system and its first-degree approximate holonomic system are given. With the aid of the structure equation that the gauge function satisfies, the exact and approximate Hojman conserved quantities deduced directly from the Lie symmetry are derived. Finally, an example is given to study the exact and approximate Hojman conserved quantity of the system. 相似文献
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梅凤翔 《应用数学和力学(英文版)》1999,20(6):629-634
In this paper, the Lie symmetries and the conserved quantities of the holonomic variable mass systems are studied. By using
the invariance of the ordinary differential equations under the infinitesimal transformations, the determining equations and
the conserved quantities are given. And an example is given to illustrate the application of the result.
Foundation item: the National Natural Science Foundation of China (19572038) 相似文献