单面非完整力学系统的Noether理论

研究具有单面非完整约束的力学系统的Noether对称性与守恒量。基于Hamilton作用量在r参数有限变换群Gr的无限小变换下的不变性,建立了系统的广义Noether定理及其逆定理,并举例说明结果的应用。     

单面非完整力学系统的Noether理论

研究具有单面非完整约束的力学系统的Noether对称性与守恒量.基于Hamilton作用量在r参数有限变换群G,的无限小变换下的不变性,建立了系统的广义Noether定理及其逆定理,并举例说明结果的应用.     

广义Noether定理和Poincare-Cartan积分不变量

指出约束在包含时间在内的正则变量的总变分下不变时,仍可导出高阶微商奇异Lagrange量系统经典正则Noether定理和Poincare-Cartan(PC)积分不变量;不同的是,在以往文献中要求约束在正则变量的等时变换下不变. 基于相空间Green函数的生成泛函,导出了高阶微商奇异Lagrange量系统在量子水平下的广义Noether定理和PC积分不变量;证明了当变换的Jacobi行列式不为1时,仍可导出量子PC积分不变量;将量子情况下的结果与经典结果作了对比.     

导数空间的变质量相对论性运动方程

在ｍ阶导数空间中,同时考虑经典变质量和相对论变质量的情况,建立了导数空间的变质量相对论性万有Ｄ′Ａｌｅｍｂｅｒｔ原理,得到了任意阶非完整系统的运动方程。     

变质量二阶线性非完整系统的广义Bertrand定理

本文给出了变质量二阶线性非完整力学系统的广义Ｂｅｒｔｒａｎｄ定理，已知上述系统的一个第一积分可确定作用在该系统上的力。文末举例说明新结果的应用。     

变质量二阶线性非完整系统的广义Bertrand定理

本文给出了变质量二阶线性非完整力学系统的广义Ｂｅｒｔｒａｎｄ定理：已知上述系统的一个第一积分可确定作用在该系统上的力。文末举例说明新结果的应用。     

相对论中变质量问题的Wittaker方程

研究相对论性非完整系统的广义能量积分存在的条件，给出用能量积分降阶相对论性非完整系统广义ЧａПｊ１БГИН方程的方法，得到相对论性广义Ｗｈｉｔｔａｋｅｒ方程，并变换到Ｎｉｅｌｓｅｎ形式打对论性广义Ｗｈｉｔｔａｋｅｒ方程。     

广义Birkhoff系统分数阶最优控制问题的Noether定理

探讨了广义Birkhoff系统分数阶最优控制问题的Noether定理。首先,基于Caputo分数阶导数提出广义Birkhoff系统的分数阶最优控制问题,并运用分数阶变分方法得到了广义Birkhoff系统的分数阶最优控制问题的极值条件。然后,运用分数阶微积分和分数阶变分方法讨论了泛函在无穷小变换群作用下的不变性,分别给出了其时间不变和时间变化情况下的分数阶最优控制问题的Noether定理。最后,应用实例显示方法的有效性。     

具有单面完整约束的动力学系统的Noether定理

以微分变分原理为出发点研究具有单面完整约束的动力学系统的守恒律,给出了单而完整约束力学系统的Noether定理,并举例说明结果的应用.     

变质量弱非完整系统相对于非惯性系的第一积分

本文首先建立了变质量弱非完整系统相对于非惯性系运动的Ｄ，Ａｌｅｍｂｅｒｔ－Ｌａｇｒａｎｇｅ原理和广义型方程，然后，研究并给出了变质量弱非完整系统相对于非惯性系运动的动力学方程在一阶近似情况下的广义循环积分和广义能量积分。文未，举两例说明结果的应用。     

Noether定理的推广及应用

给出了非定域变换下的广义Ｎｏｅｔｈｅｒ恒等式（广义Ｎｏｅｔｈｅｒ第二定理）．将其应用于规范场理论，导出了新的ＰＢＲＳＴ荷和“非定域”荷。     

转动变质量系统的相对论性Hamilton原理

建立了转动变质量质点的相对论性动力学方程,构造转动变质量系统的相对论性动力学函数Ｔ＊ｒ,给出转动了变质量系统的相对论性Ｈａｍｉｌｔｏｎ原理。     

组合旋转壳体的安定上限分析

对一般组合壳体的各个子区的位移场进行双三次Ｂ样条插值，同时对子区交界处的广义向量以单三次Ｂ样条展开，推导出以广义力向量表示的组合壳体的平衡方程，然后从Ｂｅｔｔｉ互换定理和虚功原理出发推导出离散的壳体结构中可能的塑性应变率循环，从而给出了组合壳体安定上限分析的有限元列式，把组合壳体的安定上限分析归结为求解一个数学规划问题，文末给出了算例。     

Orthogonal transformation operation theorem of a spatial universal uniform rotating magnetic field and its application in capsule endoscopy

According to the anti-phase sine current superposition theorem, the orientation, the magnetic flux density, the angular speed and the rotational direction of the spatial universal rotating magnetic field (SURMF) can be controlled within the tri-axial orthogonal square Helmholtz coils (TOSHC). Nevertheless, three coupling direction angles of the normal vector of the SURMF in the Descartes coordinate system cannot be separately controlled, thus the adjustment of the orientation of the SURMF is difficult and the flexibility of the robotic posture control is restricted. For the dimension reduction and the decoupling of control variables, the orthogonal transformation operation theorem of the SURMF is proposed based on two independent rotation angular variables, which employs azimuth and altitude angles as two variables of the three-phase sine current superposition formula derived by the orthogonal rotation inverse transformation. Then the unique control rules of the orientation and the rotational direction of the SURMF are generalized in each spatial quadrant, thus the scanning of the normal vector of the SURMF along the horizontal or vertical direction can be achieved through changing only one variable, which simplifies the control process of the orientation of the SURMF greatly. To validate its feasibility and maneuverability, experiments were conducted in the animal intestine utilizing the innovative dual hemisphere capsule robot (DHCR) with active and passive modes. It was demonstrated that the posture adjustment and the steering rolling locomotion of the DHCR can be realized through single variable control, thus the orthogonal transformation operation theorem makes the control of the orientation of the SURMF convenient and flexible significantly. This breakthrough will lay a foundation for the human-machine interaction control of the SURMF.     

ASTOVL升力风扇飞机的纵向控制系统研究

ASTOVL升力风扇飞机是多变量、强耦合、复杂的非线性系统,采用非线性动态逆理论设计控制律以实现系统的非线性对消及解耦,然后,采用线性系统的设计方法对系统进行设计,以使系统获得期望的飞行品质。同时,考虑到ASTOVL升力风扇飞机是由气动舵面和力矢量融合作用的,为了延缓各舵面进入饱和的时间,采用加权广议逆中的极小N－范数广义逆定量分配力矩指令,从而使各舵面达到适当的偏转角。并将所设计的控制律进行了仿真,结果验证了所设计的动态控制律使系统实现了非线性对消和解耦,单个指令作用时,只有该项响应,其余不受影响;所有指令作用时,其结果就等于单个指令作用时的线性叠加,这样使驾驶员的操纵大大简化而易于控制,从而大大降低了飞行事故率。     

Perturbation to Noether Quasi-Symmetry and Adiabatic Invariants for Nonholonomic Systems on Time Scales

Perturbation to Noether quasi-symmetry and adiabatic invariants for the nonholonomic system on time scales are studied. Firstly, some properties of time scale calculus are reviewed. Secondly, the differential equations of motion for the nonholonomic system on time scales, Noether quasi-symmetry and conserved quantity are given. Thirdly, perturbation to Noether quasi-symmetry and adiabatic invariants, which are the main results of this paper, are investigated. The main results are achieved by two steps, the first step is to obtain adiabatic invariants without transforming the time, and the next is to obtain adiabatic invariants under the infinitesimal transformations of both the time and the coordinates. And in the end, an example is given to illustrate the methods and results.