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研究力学系统Birkhoff动力学函数的构造方法.Santilli第二方法是目前构造Birkhoff动力学函数时常用的方法之一,但研究发现其计算公式存在冗余项.通过具体的证明得到了简化的Santilli第二方法,从而为自伴随系统Birkhoff动力学函数的构造提供了更为简洁的计算公式.举例说明结果的应用. 相似文献
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带附加项的定常一阶Lagrange系统在一定条件下可化成梯度系统,利用梯度系统的特性研究了带附加项的一阶Lagrange系统的稳定性及其对参数的依赖关系.以具体实例在参数平面上划出稳定性区域,进一步说明了参数的变化不仅可改变稳定性质,而且可改变平衡点的参数. 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
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根据偏微分方程的Cauchy-Kovalevski可积性定理,将欠定的Birkhoff方程组转化为以Birkhoff函数组为未知变量的完备的偏微分方程组,提出了构造Birkhoff动力学函数的参数调节法.通过调节补偿方程中的两类可调的函数参数就能得到不同的Birkhoff函数组.并把构造Birkhoff函数组的参数调节法与Santilli构造方法进行了比较,例如研究了利用动力学系统独立的第一积分构造Birkhoff函数组的Hojman方法与参数调节法之间的关系.最后,给出应用实例验证了参数调节法的实用性及其与Santilli 3种构造方法的关系 相似文献
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本文从高阶非完整系统嵌入变分恒等式的积分变分原理出发, 根据三种不等价条件变分的选取, 得到了高阶非完整系统的三类不等价动力学模型, 即高阶非完整约束系统的vakonomic方程、Lagrange-d'Alembert 方程和一种新的动力学方程. 当高阶非完整约束方程退化为一阶非完整约束时, 利用此理论可以得到一般非完整系统的vakonomic模型、Chetaev模型和一种新的动力学模型. 最后借助于应用实例验证了结论的正确性.
关键词:
高阶非完整约束
变分恒等式
条件变分
vakonomic动力学 相似文献
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Symmetries and conserved quantities of discrete wave equation associated with the Ablowitz-Ladik-Lattice system 下载免费PDF全文
In this paper, we present a new method to obtain the Lie symmetries and conserved quantities of the discrete wave equation with the Ablowitz-Ladik-Lattice equations. Firstly, the wave equation is transformed into a simple difference equation with the Ablowitz-Ladik-Lattice method. Secondly, according to the invariance of the discrete wave equation and the Ablowitz-Ladik-Lattice equations under infinitesimal transformation of dependent and independent variables, we derive the discrete determining equation and the discrete restricted equations. Thirdly, a series of the discrete analogs of conserved quantities, the discrete analogs of Lie groups, and the characteristic equations are obtained for the wave equation. Finally, we study a model of a biological macromolecule chain of mechanical behaviors, the Lie symmetry theory of discrete wave equation with the Ablowitz-Ladik-Lattice method is verified. 相似文献
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