Integrating Factors and Conservation Theorems for the Nonholonomic Singular Lagrange System

We present a general approach to the construction of conservation laws for the nonholonomic singular Lagrange system. Firstly, the differential equations of motion of the system are written, the definition of integrating factors is given for the system. Next, the necessary conditions for the existence of the conserved quantity are studied in detail. Finally, the conservation theorem and its inverse are established for the system, an example is given to illustrate the application of the result.     

Integrating Factors and Conservation Theorems of Lagrangian Equations for Nonconservative Mechanical System in Generalized Classical Mechanics

The conservation theorems of the generalized Lagrangian equations for nonconservative mechanical system are studied by using method of integrating factors. Firstly, the differential equations of motion of system are given, and the definition of integrating factors is given. Next, the necessary conditions for the existence of the conserved quantity are studied in detail. Finally, the conservation theorem and its inverse for the system are established, and an example is given to illustrate the application of the result.     

Integrating Factors and Conservation Theorems of Lagrangian Equations for Nonconservative Mechanical System in Generalized Classical Mechanics

The conservation theorems of the generalized Lagrangian equations for nonconservative mechanical system are studied by using method of integrating factors. Firstly, the differential equations of motion of system are given, and the definition of integrating factors is given. Next, the necessary conditions for the existence of the conserved quantity are studied in detail. Finally, the conservation theorem and its inverse for the system are established, and an example is given to illustrate the application of the result.     

Lie-Form Invariance of the Nonholonomic System of Relative Motion in Event Space

In this paper, the Lie-form invariance of a nonholonomic system of relative motion in event space is studied. Firstly, the definition and the criterion of the Lie-form invariance of the nonholonomic system of relative motion in event space is given. Secondly, the Hojman conserved quantity and a new type of conserved quantity deduced from the Lie-form invariance are obtained. An example is given to illustrate the application of the results.     

Integrating Factors and Conservation Laws for Relativistic Mechanical System

In this paper, we present a new method to construct the conservation laws for relativistic mechanical systems by finding corresponding integrating factors. First, the Lagrange equations of relativistic mechanical systems are established, and the definition of integrating factors of the systems is given; second, the necessary conditions for the existence of conserved quantities of the relativistic mechanical systems are studied in detail, and the relation between the conservation laws and the integrating factors of the systems is obtained and the generalized Killing equations for the determination of the integrating factors are given; finally, the conservation theorem and its inverse for the systems are established, and an example is given to illustrate the application of the results.     

Integrating Factors and Conservation Laws for Relativistic Mechanical System

In this paper, we present a new method to construct the conservation laws for relativistic mechanical systems by finding corresponding integrating factors. First, the Lagrange equations of relativisticmechanical systems are established, and the definition of integrating factors of the systems is given; second, the necessary conditions for the existence of conserved quantities of the relativistic mechanical systems are studied in detail, and the relation between the conservation laws and the integrating factors of the systems is obtained and the generaized Killing equations for the determination of the integrating factors are given; finally, the conservation theorem and its inverse for the systems are established, and an example is given to illustrate the application of the results.     

Integrating Factors and Conservation Laws of Generalized Birkhoff System Dynamics in Event Space

In this paper, the conservation laws of generalized Birkhoff system in event space are studied by using the method of integrating factors. Firstly, the generalized Pfaff-Birkhoff principle and the generalized Birkhoff equations are established, and the definition of the integrating factors for the system is given. Secondly, based on the concept of integrating factors, the conservation theorems and their inverse for the generalized Birkhoff system in the event space are presented in detail, and the relation between the conservation laws and the integrating factors of the system is obtained and the generalized Killing equations for the determination of the integrating factors are given. Finally, an example is given to illustrate the application of the results.     

事件空间中非完整非保守系统的守恒量存在定理及其逆定理

提出了事件空间中非完整非保守系统守恒定律构成的一般途径.首先，列写系统的运动微分方程，给出积分因子的定义.其次，详细地研究了守恒量存在的必要条件，并建立了事件空间中非完整非保守系统的守恒量存在定理及其逆定理.最后，举例说明结果的应用. 关键词： 事件空间 非完整非保守系统 积分因子 守恒定理     

用积分因子方法研究非完整约束系统的守恒律

用积分因子方法研究非线性非完整约束系统的守恒律.给出了非完整约束系统的Routh方程的积分因子的定义，研究了守恒量存在的必要条件，建立了系统的守恒定理及其逆定理，并举例说明结果的应用. 关键词： 非完整约束系统 积分因子 守恒律 Killing方程     

Existential theorem of conserved quantities and its inverse for the dynamics of nonholonomic relativistic systems

We present a general approach to the construction of conservation laws for the dynamics of nonholonomic relativistic systems.Firstly,we give the definition of integrating factors for the differential equations of motion of a mechanical system.Next,the necessary conditions for the existemce of the conserved quantities are studied in detail.Then,we establish the existential theorem for the conserved quantities and its inverse for the equations of motion of a nonholonomic relativistic system.Finally,an exampled is given to illustrate the application of the result.     

Integrating factors and conservation theorems for Hamilton‘s canonical equations of motion of variable mass nonholonmic nonconservative dynamical systems

We present a general approach to the construction of conservation laws for variable mass noholonmic nonconservative systems.First,we give the definition of integrating factors,and we study in detail the necessary conditions for the existence of the conserved quantities,Then,we establish the conservatioin theorem and its inverse theorem for Hamilton‘s canonical equations of motion of variable mass nonholonomic nonocnservative dynamical systems.Finally,we give an example to illustrate the application of the results.     

A General Approach to the Construction of Conservation Laws for Birkhoffian Systems in Event Space

For a Birkhoffing system in the event space, a general approach to the construction of conservation laws is presented. The conservation laws are constructed by finding corresponding integrating factors for the parametric equations of the system. First, the parametric equations of the Birkhoffian system in the event space are established, and the definition of integrating factors for the system is given; second the necessary conditions for the existence of conservation laws are studied in detail, and the relation between the conservation laws and the integrating factors of the system is obtained and the generalized Killing equations for the determination of the integrating factors are given; finally, the conservation theorem and its inverse for the system are established, and an example is given to illustrate the application of the results.     

Integrating factors and conservation theorem for holonomic nonconservative dynamical systems in generalized classical mechanics

In this paper,we present a general approach to the construction of conservation laws for generalized classical dynamical systems.Firstly,we give the definition of integrating factors and ,secondly,we study in detail the necessary conditions for the existence of conserved quantities.Then we establish the conservation theorem and its inverse for the hamilton‘s canonical equations of motion of holonomic nonconservative dynamical systems in generalized classical mechanics.Finally,we give an example to illustrate the application of the results.     

Noether Symmetry and Noether Conserved Quantity of Nielsen Equation for Dynamical Systems of Relative Motion

Noether symmetry of Nielsen equation and Noether conserved quantitydeduced directly from Noether symmetry for dynamical systems of the relative motion are studied. The definition and criteria of Noether symmetry of a Nielsen equation under the infinitesimal transformations of groups are given. Expression of Noether conserved quantity deduced directly from Noether symmetry of Nielsen equation for the system are obtained. Finally, an example is given to illustrate the application of the results.     

Integrating factors and conservation theorems of constrained Birkhoffian systems

In this paper the conservation theorems of the constrained Birkhoffian systems are studied by using the method of integrating factors. The differential equations of motion of the system are written. The definition of integrating factors is given for the system. The necessary conditions for the existence of the conserved quantity for the system are studied. The conservation theorem and its inverse for the system are established. Finally, an example is given to illustrate the application of the results.     

自由光通信中卫星相对运动的补偿设计

分析了不在同一轨道平面的光通信终端搭载卫星的相对运动模型,通过对终端万向节指向的补偿校正来提高扫瞄捕获概率,缩短激光链路的建立时间,并对通信过程中的接收光束在电荷藕合器件靶面坐标系中的坐标值进行修正,减弱对快速倾斜镜的高带宽限制.最后对相对运动模型进行解算,依据方案对捕获和跟踪过程的补偿设计进行数值仿真,结果表明本设计方案可以消除由于卫星相对运动引起的光束指向偏差.该方案简化了系统结构,降低了系统复杂性,减少了能量消耗,同时易于星载计算机程序实现.     

Exact Invariants and Adiabatic Invariants of Raitzin's Canonical Equations of Motion for Nonholonomic System of Non-Chetaev's Type

The exact invariants and the adiabatic invariants of Raitzin's canonical equations of motion for the nonholonomic system of non-Chetaev's type are studied. The relations between the invariants and the symmetries of the system are established. Based on the concept of higher order adiabatic invariant of mechanical system with the action of a small perturbation, the form of the exact invariants and adiabatic invariants and the conditions for their existence are proved. Finally, the inverse problem of the perturbation to symmetries of the system is studied and an example is also given to illustrate the application of the results.