论非完整系统的Hamilton原理与完整系统的Hamilton原理的统一性
On the Unification of the Hamilton Principles in Non-Holonomic System and in Holonomic System
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摘要: 本文通过典型实例和理论分析证明了:在有势力作用下,对于非完整系统Hamilton原理同样有像完整系统那样使Lagrange函数取驻值的形式;使Lagrange函数变分对时间积分为零的形式是前者的演变形式;因此,两种形式是统一的。
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关键词:
- 非完整系统 /
- 完整系统 /
- Hamilton原理 /
- 真实轨道 /
- 测地轨道
Abstract: In this paper by means of typical engineering examples and deep theoretical analysis, we prove that under the effect of conservative force, the Hamilton principles in holonomic and non-holonomic systems have the same formula δ∫Ldt=0. The formula ∫δdt=0 is an evolved form of the formula δ∫Ldt=0. Therefore, the two formulas are unified.-
Key words:
- non-holonomic system /
- holonomic system /
- the Hamilton /
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[1] L.A.Pats,Variation principles in dynamics,J.Mech.and Appl.Math.,7,3 (1954),338-351. [2] V.V.Rumjantsev,On the Hamilton principle for non-holonomic systems,Appl.Math.and Mech.,42,3 (1978),387-399. [3] 钱伟长,《变分法及有限元》,科学出版社(1980). [4] 胡海昌,《弹性力学变分原理及其应用》,科学出版社(1981). -
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