Lie Symmetry and Hojman Conserved Quantity of Maggi Equations

Lie symmetry of Maggi equations is studied. Its determining equation and restriction equation of nonholonomic constraint are given. A Hojman conserved quantity can be deduced directly by using the Lie symmetry. An example is given to illustrate the application of the result.     

On Chaotification of Discrete Hamilton Systems

The chaotification problem of discrete Hamilton systems in one dimensional space is investigated and corresponding chaotification theorem is established. Feedback control techniques is used to make arbitrary discrete Hamilton systems chaotic, or enhance its existing chaotic behaviors. By designing a universal controller and combining anti-integrable limit it is proved that chaos of the controlled systems is in the sense of Devaney. In particular, the systems corresponding to the original systems and designed controllers are only required to satisfy some mild assumptions. Moreover, the range of the coefficient of the controller is given.     

高阶Maggi方程的Birkhoff化及其辛算法

针对非完整系统的高阶Maggi方程,在满足一定的条件时,可以对其进行Birkhoff化.通过构造生成函数,利用Birkhoff广义辛算法对其进行数值仿真.仿真结果和传统的Runge Kutta算法结果相比较,Birkhoff广义辛算法在长期跟踪后更加准确.     

非完整系统Appell方程的保辛算法研究

本文利用待定张量法对非完整系统Appell方程进行Birkhoff化,并根据生成函数的构造原理确定生成函数,给出Birkhoff辛格式,最后通过具体的Appell方程算例进行理论验证和仿真模拟,从一定程度上说明了保辛算法随着时间演变更具有效性和优越性.     

确立新的质量观促进“高等数学”的教学改革

高教改革的中心是提高教育、教学质量,“高等数学”是大学的一门具有启蒙性质的重要基础课,一方面是为后续课程打基础,另一方面是培养学生的科学素质,实现学生在素质上由中学向大学转变。围绕“因材施教的多元质量观”,我们对“高等数学”的教学方法、教学手段进行了更深入的研究,对深化高教改革也有很好的推动作用。     

无结构内阻尼磁性刚体航天器姿态动力学稳定性分析

在地球万有引力场和磁场中，考虑大气阻力的条件下，讨论无结构内阻尼的磁性刚体航天器在圆轨道上出现的混沌问题．根据动量矩定理建立动力学模型，利用Melnikov方法证明发生混沌的可能性，并利用数值仿真分析了系统的动力学行为．理论结果与数值仿真结果相一致．     

Weak Noether symmetry and conserved laws of Birkhoffian systems

A new kind of weak Noether symmetry is obtained that arises in the study of Birkhoffian systems.The conserved quantities,which includes Noether conserved quantity,Hojman type conserved quantity and new type conserved quantity,are also calculated from this symmetry.Finally,two examples are presented to illustrated the application of these new results.