本文引入了 m 阶导数空间及与之相应的广义坐标的概念,将原相对于3N维 Euclid 空间“E_(3N)”的 m 阶非完整系统变为 m 阶导数空间“中形式上的完整系统,导出了包含万有 D'Alembert——Lagrange 微分原理在内的任意阶非完整系统的新...本文引入了 m 阶导数空间及与之相应的广义坐标的概念,将原相对于3N维 Euclid 空间“E_(3N)”的 m 阶非完整系统变为 m 阶导数空间“中形式上的完整系统,导出了包含万有 D'Alembert——Lagrange 微分原理在内的任意阶非完整系统的新型 Appell 方程和广义的 D'Alembert 原理。展开更多
A proof was given here to show that the inertial forces in a noninertial system are not fabricated forces, but potential forces which actually act on the objects in motion in the acceleration field, according to the e...A proof was given here to show that the inertial forces in a noninertial system are not fabricated forces, but potential forces which actually act on the objects in motion in the acceleration field, according to the equivalent principle between gravitation and inertial forces in the theory of general relativity. Furthermore, the invariance of kinetic equation was illuminated also.展开更多
As a concrete application of the concepts of 'derivative space' and'correspondent kinetic energy' in derivative space, and of foe thought of 'treatingnonholonomic systems by changing them into form...As a concrete application of the concepts of 'derivative space' and'correspondent kinetic energy' in derivative space, and of foe thought of 'treatingnonholonomic systems by changing them into formal holonomic system' which theauthors have previously proposed in references [1. 2, 3]. this paper derived another newuniversal D'Alembert principle and a new Maggi equation for arbitrary ordernonholonomic mechanical systems. An example using the Maggi equation is given.展开更多
The important development has been made in studying nonholonomic systems, but many theoretical and practical problems still need to be solved. In order to suit development of analytical mechanism itself and the need o...The important development has been made in studying nonholonomic systems, but many theoretical and practical problems still need to be solved. In order to suit development of analytical mechanism itself and the need of wide-ranging application to other subjects and modem engineering technology, its research method, the mathematical models got with this method and final forms of differential equations of motion still need to be further studied. This article gives up the traditional method which was used to study the nonholonomic systems in 3N dimensional Euclid space "E<sub>3N</sub>".展开更多
文摘本文引入了 m 阶导数空间及与之相应的广义坐标的概念,将原相对于3N维 Euclid 空间“E_(3N)”的 m 阶非完整系统变为 m 阶导数空间“中形式上的完整系统,导出了包含万有 D'Alembert——Lagrange 微分原理在内的任意阶非完整系统的新型 Appell 方程和广义的 D'Alembert 原理。
文摘A proof was given here to show that the inertial forces in a noninertial system are not fabricated forces, but potential forces which actually act on the objects in motion in the acceleration field, according to the equivalent principle between gravitation and inertial forces in the theory of general relativity. Furthermore, the invariance of kinetic equation was illuminated also.
文摘As a concrete application of the concepts of 'derivative space' and'correspondent kinetic energy' in derivative space, and of foe thought of 'treatingnonholonomic systems by changing them into formal holonomic system' which theauthors have previously proposed in references [1. 2, 3]. this paper derived another newuniversal D'Alembert principle and a new Maggi equation for arbitrary ordernonholonomic mechanical systems. An example using the Maggi equation is given.
文摘The important development has been made in studying nonholonomic systems, but many theoretical and practical problems still need to be solved. In order to suit development of analytical mechanism itself and the need of wide-ranging application to other subjects and modem engineering technology, its research method, the mathematical models got with this method and final forms of differential equations of motion still need to be further studied. This article gives up the traditional method which was used to study the nonholonomic systems in 3N dimensional Euclid space "E<sub>3N</sub>".
