关于Bertrand一个定理的推广*
On a Generalization of Bertrand’s Theorem
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摘要: 本文将Bertrand的一个定理:已知完整系统的一个第一积分可确定作用在系统上的力,推广到非完整力学系统.并举例说明新结果的应用.Abstract: Bertrand's theorem for the determination of the applied forces to a holonomic system from one of its first integrals, is extended to nonholonomic systems. Some interesting applications of this new result are also given.
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Key words:
- analytical mechanics /
- nonholonomic system /
- first integral /
- inverse problem of dynamics
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[1] Whittaker,E.T.,A Treatise on the Analytical Dynamics of Particles and Rigid Bodies,Fourth edition,Cambridge Press(1952). [2] Галиллин А.С.,Мемобы Решенця Обрамных Забач Дцнамцкц,М.,Наука(1986). [3] Еругин Н.П.,Построение всего множества систм дмфференциалъных уравнений,имеющих заданную интегралъную крзвую,П,М,М.,16(6)(1952),659-670. [4] 梅凤翔.《非完整系统力学基础》.北京工业学院出版社(1985).
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