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| Non-contemporaneous variations and Hlder's principle | |
| 引用本文： | 梁立孚,胡海昌,刘石泉.Non-contemporaneous variations and Hlder''''s principle[J].中国科学G辑(英文版),2003,46(5). |
| 作者姓名： | 梁立孚 胡海昌 刘石泉 |
| 作者单位： | Space Engineering Department of Harbin Engineering University，Harbin 150001，China，Chinese Academy of Space Technology Institute of Spacecraft System Engineering，Beijing 100086，China，China Sanjiang Space Industry Group Corporation，Wuhan 430015，China |
| 基金项目： | 国家自然科学基金，黑龙江省自然科学基金 |
| 摘 要： | In the process of deducing the Holder principle, a key step is to use the concept of non-contemporaneous variations. In this paper, whether starting from analytic method or from graphic solution method, the authors prove that the expression formula of non-contemporaneous variations is incorrect when the variable functions have zero-order nearness degree, and obtain a new expression. From the view of calculus of variations and differential calculus, the non-contemporaneous variations are studied. The study result shows that the concept of non-contemporaneous variations is a combination of the concept of variations and the concept of differentiation. The authors prove that the new expression is correct and obtain an equivalent expression of it. By means of this equivalent expression, this paper proves that the above expression formula of non-contemporaneous variations is correct when the variable functions have one-order nearness degree. Further study shows that, in the process of deducing Holder's princi |
Non-contemporaneous variations and Holder's principle |
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| LIANG Lifu HU Haichang & LIU Shiquan,Space Engineering.Non-contemporaneous variations and Holder''''s principle[J].Science in China(Physics Astronomy),2003,46(5). | |
| Authors: | LIANG Lifu HU Haichang & LIU Shiquan Space Engineering |
| Institution: | 1. Space Engineering Department of Harbin Engineering University, Harbin 150001, China 2. Chinese Academy of Space Technology Institute of Spacecraft System Engineering, Beijing 100086, China 3. China Sanjiang Space Industry Group Corporation, Wuhan 430015, China |
| Abstract: | In the process of deducing the Holder principle, a key step is to use the concept of non-contemporaneous variations. In this paper, whether starting from analytic method or from graphic solution method, the authors prove that the expression formula of non-contemporaneous variations is incorrect when the variable functions have zero-order nearness degree, and obtain a new expression. From the view of calculus of variations and differential calculus, the non-contemporaneous variations are studied. The study result shows that the concept of non-contemporaneous variations is a combination of the concept of variations and the concept of differentiation. The authors prove that the new expression is correct and obtain an equivalent expression of it. By means of this equivalent expression, this paper proves that the above expression formula of non-contemporaneous variations is correct when the variable functions have one-order nearness degree. Further study shows that, in the process of deducing Holder's principle, there is an implicit expression. Whether starting from analytic method or from graphic solution method, the authors discovered that the implicit expression of non-contemporaneous variations is incorrect when the variable functions have zero-order nearness degree and have one-order nearness degree. This paper proves that the implicit expression of non-contemporaneous variations is correct when the variable functions have two-order nearness degree. Further study shows that Holder's principle is tenable when the variable functions have two-order nearness degree. |
| Keywords: | differentiation variation non-contemporaneous variations non-holonomic systems |
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