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本文首先讨论了Hamilton系统与Birkhoff系统的关系,以及Birkhoff系统研究的理论意义和实际价值.进一步研究了非齐次Hamilton系统的Birkhoff化理论、Birkhoff方程的实现条件、构造方法,指出了Birkhoff动力学研究的主要困难和未来应该重点关注的基本问题;最后给出了广义Birkhoff系统动力学方程的形式以及研究广义Birkhoff方程的重要意义,并探讨了赝广义Birkhoff方程的形式以及构造动力学系统赝广义Birkhoff方程的目的和意义. 相似文献
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Geometric formulations and variational integrators of discrete autonomous Birkhoff systems 下载免费PDF全文
The variational integrators of autonomous Birkhoff systems are obtained by the discrete variational principle. The geometric structure of the discrete autonomous Birkhoff system is formulated. The discretization of mathematical pendulum shows that the discrete variational method is as effective as symplectic scheme for the autonomous Birkhoff systems. 相似文献
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采用水热法添加十二烷基硫酸钠(SDS)成功制备了体心立方In(OH)3片层酥状粉体。用X射线衍射(XRD)、场发射扫描电子显微镜(FESEM)对产物进行了表征,研究了SDS对In(OH)3尺寸和形貌的影响,并探讨了In(OH)3晶体生长机理。结果表明:在低浓度SDS下得到了分散性较好的千层酥囊状In(OH)3粉体,在高浓度SDS下得到分散性较好的片状In(OH)3粉体。平面状的In3+聚集体超过临界值形成晶核,晶核沿着[100]晶体学方向长大,In(OH)3晶体按二维层状生长最终形成In(OH)3薄片。 相似文献
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就一般非完整约束系统,从约束方程满足的变分恒等式出发,利用增广位形流形上的向量场定义三类非自由变分,即非完整变分:vakonomic变分、Hlder变分、Suslov变分,并讨论它们之间的关系以及它们成为自由变分的充要条件.利用非完整变分以及相应的积分变分原理建立两类动力学方程:vakonomic方程和Routh方程或Chaplygin方程.通过vakonomic方程分别与Routh方程和Chaplygin方程比较,得到它们具有共同解的两类充分必要条件.这些条件并不是约束的可积性条件.
关键词:
非完整约束
非完整变分
Chetaev条件
vakonomic动力学 相似文献
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This paper discusses the conformal invariance by infinitesimal
transformations of canonical Hamilton systems. The necessary and
sufficient conditions of conformal invariance being Lie symmetrical
simultaneously by the action of infinitesimal transformations are
given. The determining equations of the conformal invariance are
gained. Then the Hojman conserved quantities of conformal invariance
by special infinitesimal transformations are obtained. Finally an
illustrative example is given to verify the results. 相似文献
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采用分子动力学方法研究了N2分子在强激光场作用下的经典轨迹,并应用了现在较优越的数值方法——辛算法来求解方程,这使计算结果更加令人信服.通过对强激光场作用下N2分子的研究,我们得到了在极端条件下同核双原子分子的动力学特点. 相似文献
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A necessary and sufficient condition for transforming autonomous systems into linear autonomous Birkhoffian systems 下载免费PDF全文
The problem of transforming autonomous systems into Birkhoffian systems is studied. A reasonable form of linear autonomous Birkhoff equations is given. By combining them with the undetermined tensor method, a necessary and sufficient condition for an autonomous system to have a representation in terms of linear autonomous Birkhoff equations is obtained. The methods of constructing Birkhoffian dynamical functions are given. Two examples are given to illustrate the application of the results. 相似文献