共查询到18条相似文献,搜索用时 62 毫秒
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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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针对广义Birkhoff系统动力学,提出广义Birkhoff系统动力学的一类逆问题,研究由已知积分流形来建立广义Birkhoff方程. 这类逆问题的解通常不是唯一的,需给出必要的补充要求. 最后举例说明结果的应用.
关键词:
广义Birkhoff系统
动力学逆问题
积分流形 相似文献
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研究运动微分方程Birkhoff表示的Lagrange像.得出二阶Lagrange函数应满足的条件,在此条件下广义Lagrange方程为二阶微分方程组;提出新的求解Lagrange力学逆问题路线;指出在此问题研究中曾发生过的失误.举例说明所得结果的应用. 相似文献
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讨论了构造Birkhoff表示的Hojman方法.利用该方法重新研究Birkhoff对称性,提出一种关于该对称性的新见解,给出Birkhoff守恒量的新证明,并对该守恒量仅与Birkhoff张量相关作出解释.举例说明所得结果的应用. 相似文献
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研究Birkhoff系统的约化.首先,列出系统的运动微分方程及其循环积分;其次,构造Birkhoff系统的Routh函数组,利用循环积分约化Birkhoff系统的运动微分方程,并使约化后的动力学方程仍保持Birkhoff方程的形式;最后,举例说明结果的应用.
关键词:
Birkhoff系统
约化
循环积分 相似文献
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The aim of this paper is to give a formulation of the dynamics of nonlinear RLC circuits as a geometric Birkhoffian system and to discuss in this context the concepts of regularity, conservativeness, dissipativeness. An RLC circuit, with no assumptions placed on its topology, will be described by a family of Birkhoffian systems, parameterized by a finite number of real constants which correspond to initial values of certain state variables of the circuit. The configuration space and a special Pfaffian form, called the Birkhoffian, are obtained from the constitutive relations of the resistors, inductors and capacitors involved and from Kirchhoff’s laws. Under certain assumptions on the voltage–current characteristic for resistors, it is shown that a Birkhoffian system associated with an RLC circuit is dissipative. For RLC networks which contain a number of pure capacitor loops or pure resistor loops the Birkhoffian associated is never regular. A procedure for reducing the original configuration space to a lower dimensional one, thereby regularizing the Birkhoffian, it is also presented. In order to illustrate the results, specific examples are discussed in detail. 相似文献
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给出两种构造一阶系统Birkhoff表示的新方法,可以从微分方程直接计算得到Birkhoff函数B和Birkhoff函数组Rμ. 举例说明所得结果的应用.
关键词:
分析力学
Birkhoff方程
Birkhoff表示
一阶微分方程 相似文献
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通过在蔡氏电路的耦合电阻支路中串联一个电感,采用压控忆阻替换蔡氏电路中的蔡氏二极管,提出了一种新颖的五阶压控忆阻蔡氏混沌电路.建立该电路的数学模型,从理论上分析了平衡点及其稳定性的演化过程.特别地,该电路在给定参数下只有一个不稳定的零平衡点,却形成了混沌与周期的非对称吸引子共存的吸引盆,意味着双稳定性的存在.进而利用数值仿真与PSIM电路仿真着重研究了本文电路在不同初始状态下产生的双稳定性现象及其形成机理.PSIM电路仿真结果与数值仿真结果一致,较好地验证了理论分析.借助分岔图、李雅普诺夫指数、相轨图和吸引盆进一步深入探讨了归一化五阶压控忆阻蔡氏系统依赖于系统初始条件的动力学行为.结果表明,该忆阻蔡氏系统在不同的初始条件下能够呈现出混沌吸引子与周期极限环共存的双稳定性现象. 相似文献
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This paper presents an inverse problem in analytical dynamics. The
inverse problem is to construct the Lagrangian when the integrals of
a system are given. Firstly, the differential equations are obtained
by using the time derivative of the integrals. Secondly, the
differential equations can be written in the Lagrange equations
under certain conditions and the Lagrangian can be obtained.
Finally, two examples are given to illustrate the application of the
result. 相似文献
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洪德耦合相互作用是导致多轨道体系发生轨道选择Mott相变的重要因素之一. 通过调控洪德耦合相互作用来研究其不同组成部分对轨道选择Mott相变的作用. 利用基于Lanczos 求解器的动力学平均场理论, 对比了双轨道的J模型和Jz模型的金属-绝缘体相变, 并重点讨论洪德耦合中的自旋翻转项和电子对跃迁项以及轨道宽度比值W2/W1如何影响轨道选择Mott 相变. 在J模型的相图中, Mott选择相占有较大的区域, 而Jz模型的轨道选择Mott 相只存在于一个很狭窄的区域内, 这说明自旋翻转项及电子对跳跃项是有利于轨道选择Mott相变发生的关键因素. 此外当轨道宽度之比大于W2/W1=0.7时, Jz 模型的轨道选择Mott 相会完全消失, 而J模型中只要轨道宽度不同都存在轨道选择Mott相. 因而, 简化后的Jz 模型只是在特定条件下才适合于研究轨道选择Mott相变. 相似文献
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Rong Huang 《Journal of synchrotron radiation》2011,18(6):930-937
One of the challenges of tuning bimorph mirrors with many electrodes is that the calculated focusing voltages can be different by more than the safety limit (such as 500 V for the mirrors used at 17‐ID at the Advanced Photon Source) between adjacent electrodes. A study of this problem at 17‐ID revealed that the inverse problem of the tuning in situ, using X‐rays, became ill‐conditioned when the number of electrodes was large and the calculated focusing voltages were contaminated with measurement errors. Increasing the number of beamlets during the tuning could reduce the matrix condition number in the problem, but obtaining voltages with variation below the safety limit was still not always guaranteed and multiple iterations of tuning were often required. Applying Tikhonov regularization and using the L‐curve criterion for the determination of the regularization parameter made it straightforward to obtain focusing voltages with well behaved variations. Some characteristics of the tuning results obtained using Tikhonov regularization are given in this paper. 相似文献
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Muhammad Asif Zahoor Raja 《中国物理 B》2014,23(1):18903-018903
In this study, stochastic computational intelligence techniques are presented for the solution of Troesch’s boundary value problem. The proposed stochastic solvers use the competency of a feed-forward artificial neural network for mathematical modeling of the problem in an unsupervised manner, whereas the learning of unknown parameters is made with local and global optimization methods as well as their combinations. Genetic algorithm(GA) and pattern search(PS) techniques are used as the global search methods and the interior point method(IPM) is used for an efficient local search. The combination of techniques like GA hybridized with IPM(GA-IPM) and PS hybridized with IPM(PS-IPM) are also applied to solve different forms of the equation. A comparison of the proposed results obtained from GA, PS, IPM, PS-IPM and GA-IPM has been made with the standard solutions including well known analytic techniques of the Adomian decomposition method, the variational iterational method and the homotopy perturbation method. The reliability and effectiveness of the proposed schemes, in term of accuracy and convergence, are evaluated from the results of statistical analysis based on sufficiently large independent runs. 相似文献