Search

Structural equation and Mei conserved quantity of Mei symmetry for Appell equations in holonomic systems with unilateral constraints are investigated. Appell equations and differential equations of motion for holonomic mechanic systems with unilateral constraints are established. The definition and the criterion of Mei symmetry for Appell equations in holonomic systems with unilateral constraints under the infinitesimal transformations of groups are also given. The expressions of the structural equation and Mei conserved quantity of Mei symmetry for Appell equations in holonomic systems with unilateral constraints expressed by Appell functions are obtained. An example is given to illustrate the application of the results.

The Mei symmetry and Mei conserved quantity of the Nielsen equation for a non-Chetaev-type non-holonomic non-conservative system are studied. The differential equations of motion of the Nielsen equation for the system, the definition and the criterion of Mei symmetry and the condition and the form of Mei conserved quantities deduced directly from the Mei symmetry for the system are obtained. Finally, an example is given to illustrate the application of the results.

Based on the theory of attractive volume of lightning and combined with the parameters of exiting transmission lines of the Pearl River Delta region, the statistical method of single — span corridor was established. The lightning location data of corridor area of transmission line under different terrain environment, such as the mountains, and plain terrain, were selected. The distribution of lightning activity and amplitude probability of lightning current before and after the erection of HV transmission lines was analyzed. And bas ed on finite element-charge simulation method, numerical calculation and simulation of the electrostatic field of lightning leader and ground was established before and after the erection of HV transmission Tower; According to the principles of the development path of lightning and the strongest electric field with the same direction, the physical process of impact of distribution of ground flash caused by the erection of transmission lines was analyzed. The results s how that in the same voltage transmission line, there exited a large impact of ground flash activity in different terrain env ironment on the erection of transmission lines and electrical tower.

For a holonomic system in relative motion, the conformal invariance and the conserved quantity of Mei symmetry with Appell equations are investigated. First, by using the infinitesimal one-parameter transformation group and the infinitesimal generator vector, the definitions of Mei symmetry and the conformal invariance with Appell equations in a holonomic system in relative motion are given, and the determining equations of the conformal invariance of Mei symmetry for the system are derived. Relationship between the conformal invariance and Mei symmetry for the system is mainly studied. Then, by means of the structural equation which the gauge function satisfies, the expression of Mei conserved quantity deduced from Mei symmetry for the system is obtained. Finally, an example is given to illustrate the application of the result.

Stray radiation is an important indicator for the infrared optical systems involved in the process of designing and testing. In order to measure the internal stray radiation in infrared imaging systems, a method based on radiometric calibration is proposed, and its rationality is verified by theoretical analysis and experiments. Firstly, the model of radiometric calibration without lens, in other words the detector for absorbing the radiation flux directly from the calibration reference source, is developed to show the influence of internal factors of the detector on the system output. Then it is compared with the results of calibration of the infrared system with a lens to obtain the system output results from the optical system, namely the internal stray radiation caused by the optical system. Finally, experiments are performed to prove the correctness of the theories proposed in this paper. The proposed method has some advantages, such as simple operation, low demand for the experimental conditions, and the capability of measuring the internal stray radiation accurately. It can be used to guide the stray radiation suppression in the process of infrared system designing, to verify the stray radiation analysis results, and to test whether the stray radiation level meets the practical requirements.

Form invariance and Mei conserved quantity for generalized Hamilton systems after adding additional terms are studied. By introducing infinitesimal transformation group and its infinitesimal transformation vector of generators, the definition and determining equations of the Mei symmetry for generalized Hamilton systems after adding additional terms are provided. By means of the structure equation satisfied by the gauge function, the Mei conserved quantity corresponding to the form invariance for the system is derived. Finally an illustrative example is given to verify the results.

The conformal invariance and Hojman conserved quantity of Lie symmetry for Appell equations in a holonomic system are studied. Under the special infinitesimal transformations in which the time is not variable, the Lie symmetry and conformal invariance of differential equations of motion for a holonomic system are defined, and the determining equations of the conformal invariance of Lie symmetry and the Hojman conserved quantity for the system are given. Finally, an example is presented to illustrate the application of the results.

Conformal invariance and conserved quantity of Mei symmetry for Appell equations of nonholonomic system of Chetaev's type with variable mass are studied. The conformal invariance and Mei symmetry for Appell equations of nonholonomic systems of Chetaev's type with variable mass are defined under the infinitesimal transformation of group, and the determining equations of conformal invariance of Mei symmetry for the system are given. Then, the expression of the corresponding conserved quantity of the system is derived. Finally, an example is given to illustrate the application of the results.

Generalized Lie symmetry and generalized Hojman conserved quantity of Appell equations for a variable mass holonomic system in relative motion are studied. The determining equation of generalized Lie symmetry of Appell equations for a variable mass holonomic system in relative motion under the infinitesimal transformations of groups is given. The expression of generalized Hojman conserved quantity deduced directly from generalized Lie symmetry for a variable mass holonomic system in relative motion is gained. Finally, the problem of dynamical system with three degree of freedom is studied by using the results of this paper.

For a holonomic system, the conformal invariance and conserved quantity of Mei symmetry for Appell equations are studied. Firstly, by the infinitesimal one-parameter transformation group and the infinitesimal generator vector, we define Mei symmetry and conformal invariance of differential equations of motion for holonomic system, and the determining equation of Mei symmetry and conformal invariance for holonomic system are given. Then, taking advantage of a structure equation that gauge function satisfies, the system corresponding Mei conserved quantity is derived. Finally, an example is given to illustrate the application of the result.

A type of new conserved quantity deduced from Mei symmetry of Appell equations for a holonomic system with unilateral constraints is investigated. The expressions of new structural equation and new conserved quantity deduced from Mei symmetry of Appell equations for a holonomic system with unilateral constraints expressed by Appell functions are obtained. An example is given to illustrate the application of the results.

Mei symmetry and Mei conserved quantity of Appell equations for a variable mass holonomic system are investigated. Appell equations and differential equations of motion for a variable mass holonomic system are established. A new expression of the total first derivative of the function with respect of time t along the systematic motional track curve, and the definition and the criterion of Mei symmetry for Appell equations under the infinitesimal transformations of groups are given. The expressions of the structural equation and Mei conserved quantity for Mei symmetry in Appell are obtained. An example is given to illustrate the application of the results.

Type Ⅲ structural equation and Mei conserved quantity of Mei symmetry for a Lagrangian system are studied. Under the infinitesimal transformation of groups, type Ⅲ structural equation and Mei conserved quantity of Mei symmetry for a Lagrangian system are obtained from the definition and the criterion of Mei symmetry for a Lagrangian system. Finally, an example is given to illustrate the application of the results.

Structural equations and Mei conserved quantity of Mei symmetry for Appell equations in a holonomic system with redundant coordinates are studied. Some aspects, including the differential equations of motion, the definition and the criterion of Mei symmetry, the form of structural equations and Mei conserved quantity of Mei symmetry of Appell equations for a holonomic system with redundant coordinates, are also investigated. Finally, an example is given to illustrate the application of the results.