Whittaker方程对非完整力学系统的推广
Extension of the Whittaker Equations to Non Holonomic Mechanical Systems
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摘要: 1904年Whittaker利用能量积分将一个完整保守力学系统问题降阶为一个带有较少自由度系统问题.并得到了Whittaker方程[1].本文推导对于非完整力学系统的这类方程.并称之为广义Whittaker方程;然后把这些方程变换为Nielsen形式;最后举例说明新方程的应用.Abstract: In 1904,using the energy integral Whittaker studied the redaction of a dynamical problem to a problem with fewer degrees of freedom for the holonomic conservative systems and obtained the Whittaker equations[1].In this articfe, the Whittaker equations are extended to non-holonomic systems and the generalized Whittaker equations are obtained And then these equations are transformed to Nielsen's form. Finally an example a given.
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[1] Whittaker,E,T.A Treatise on the Anahtical Dgnamics of Particles and Rigid Bodies,Combrige University Press(1965) [2] Четаев,Н.Г.,О П рцнчцпе Даусса,Изв,Мат.,Coc,6(1933),68-71. [3] Новоселов,В.С.,ВарцачцоннЫе Мемобы э Механцке,Ленинград(1966). [4] 梅凤翔.非完整系统力学中的交换关系,力学与实践,1,3(1979) [5] Mei Feng-siang,Nouvelles,quations du mouvement des systèmes mėcaniques non-holonomes,These d'Etat,Mai(1982),Nantes,France [6] Losco.L.M.Langlois,Seminaires de 1'Universitėde Zürich.Ivlai-Juin(1981) -
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