The Method of Derivation of Mac-Millan’s Equation for the Non-Linear Non-Holonomic System

Qiu Rong

Volume 17 Issue 6

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Article Navigation > Applied Mathematics and Mechanics > 1996 > 17(6): 559-561

Qiu Rong. The Method of Derivation of Mac-Millan’s Equation for the Non-Linear Non-Holonomic System[J]. Applied Mathematics and Mechanics, 1996, 17(6): 559-561.

Citation:

Qiu Rong. The Method of Derivation of Mac-Millan’s Equation for the Non-Linear Non-Holonomic System[J]. Applied Mathematics and Mechanics, 1996, 17(6): 559-561.

Citation:

Qiu Rong. The Method of Derivation of Mac-Millan’s Equation for the Non-Linear Non-Holonomic System[J]. Applied Mathematics and Mechanics, 1996, 17(6): 559-561.

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The Method of Derivation of Mac-Millan’s Equation for the Non-Linear Non-Holonomic System

Qiu Rong

Department of Physics, Fuzhou Uniuersity, Fuzhou 350002, P. R. China

Received Date: 1995-02-22
Rev Recd Date: 1995-11-06
Publish Date: 1996-06-15

Abstract

Abstract

The Mac-Millan's equation for the non-linear non-holongmic system in one order is derived by using only principle of differential variation of Jourdain. Therefore definition of Niu Qinping for the virtual displacentent is unnecessary. This is the natural deduetion of the method in this paper and so with the non-linear and non holonomic system in high order.
- non-linear and non-holonomic systemMac-Millan’s equation,
- definition of Niu Qinping,
- virtual displacement,

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References(7)

References

[1]	梅凤翔,Mac-Millan方程对非线性非完整力学系统的推广,应用数学和力学,5(5) (1984),665-672,
[2]	梅凤翔,《非完整系统力学基础》,北京工业学院出版社(1985), 109-111,
[3]	邱荣,Mac-Millan方程的推广,应用数学和力学,11(5) (1990), 463-466,
[4]	邱荣,非惯性系中的高阶非完整系统的Mac-Millan方程,福州大学学报(自然科学版),21(1)(1994).
[5]	邱荣,推广Mac-Millan方程到变质量力学系统,《全国第五届数学物理力学高新技术学术讨论会论文集》,西南交通大学出版社(1994), 270-277
[6]	陈立群,广义Mac-Millan方程对变质量非完整系的推广,固体力学学报,11(3) (1990),278-283.
[7]	陈立群,变质量高阶非完整系统广义Mac-Millan方程的准坐标形式,兵工学报,(2) (1992),86-91

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