THE COMPLEMENTARY PROPERTY OF LINDELÖF’S WORK AND CHAPLYGIN’S WORK

Applied Mathematics and Mechanics (English Edition) ›› 2000, Vol. 21 ›› Issue (8): 937-946.

THE COMPLEMENTARY PROPERTY OF LINDELÖF’S WORK AND CHAPLYGIN’S WORK

梁立孚, 陈卫东

Department of Airspace Engineering, Harbin Engineering University, Harbin 150001, P.R.China

收稿日期:1999-05-26 修回日期:2000-04-13 出版日期:2000-08-18 发布日期:2000-08-18
通讯作者: CHENG Chang-jun
基金资助:
the National Natural Science Foundation of China (19872022);the Doctoral Foundation of Education Committee of China

THE COMPLEMENTARY PROPERTY OF LINDELÖF’S WORK AND CHAPLYGIN’S WORK

LIANG Li-fu, CHEN Wei-dong

Department of Airspace Engineering, Harbin Engineering University, Harbin 150001, P.R.China

Received:1999-05-26 Revised:2000-04-13 Online:2000-08-18 Published:2000-08-18
Supported by:
the National Natural Science Foundation of China (19872022);the Doctoral Foundation of Education Committee of China

摘要/Abstract

摘要： Lindelf’s equation is derived by using the Vakonomic model,which shows that Lindelf’s work coincides with Vakonomic model. Chaplygin’s equation is derived by using Chetaev’s model, which shows that Chaplygin’s work coincides with Chetaev’s model. On basis of these, by improving the expressions of Chaplygin’s equation and Lindelf’s equation, the reasonable transition from Chaplygin’s equation to Lindelf’s equation is realized, the reasonable transition from Lindelf’s equation to Chaplygin’s equation is realized too. Finally, a typical example is given. The work of this paper shows that, just as the Vakonomic model and Chetaev’s model are complementary to each other, Lindelf’s work and Chaplygin’s work are complementary to each other too.

Abstract: Lindelf’s equation is derived by using the Vakonomic model,which shows that Lindelf’s work coincides with Vakonomic model. Chaplygin’s equation is derived by using Chetaev’s model, which shows that Chaplygin’s work coincides with Chetaev’s model. On basis of these, by improving the expressions of Chaplygin’s equation and Lindelf’s equation, the reasonable transition from Chaplygin’s equation to Lindelf’s equation is realized, the reasonable transition from Lindelf’s equation to Chaplygin’s equation is realized too. Finally, a typical example is given. The work of this paper shows that, just as the Vakonomic model and Chetaev’s model are complementary to each other, Lindelf’s work and Chaplygin’s work are complementary to each other too.

中图分类号:

O316

梁立孚;陈卫东. THE COMPLEMENTARY PROPERTY OF LINDELÖF’S WORK AND CHAPLYGIN’S WORK[J]. Applied Mathematics and Mechanics (English Edition), 2000, 21(8): 937-946.

LIANG Li-fu;CHEN Wei-dong . THE COMPLEMENTARY PROPERTY OF LINDELÖF’S WORK AND CHAPLYGIN’S WORK[J]. Applied Mathematics and Mechanics (English Edition), 2000, 21(8): 937-946.

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THE COMPLEMENTARY PROPERTY OF LINDELÖF’S WORK AND CHAPLYGIN’S WORK

THE COMPLEMENTARY PROPERTY OF LINDELÖF’S WORK AND CHAPLYGIN’S WORK

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