北京雁栖湖应用数学研究院 北京雁栖湖应用数学研究院

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关于我们
院长致辞
理事会
协作机构
参观来访
人员
管理层
科研人员
博士后
来访学者
行政团队
学术研究
研究团队
公开课
讨论班
招生招聘
教研人员
博士后
学生
会议
学术会议
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学院生活
住宿
交通
配套设施
周边旅游
新闻
新闻动态
通知公告
资料下载
清华大学 "求真书院"
清华大学丘成桐数学科学中心
清华三亚国际数学论坛
上海数学与交叉学科研究院
BIMSA > Nonstandard topics in classical mechanics
Nonstandard topics in classical mechanics
The proposed course of lectures will cover the parts of classical mechanics that are not included in the standard textbooks and in the courses of theoretical mechanics including:
absolute, relative and conditional integral and tensor invariants, Dirac mechanics, Nambu mechanics, vakonomic mechanics, constrained mechanical systems, nonholonomic mechanics, geometric optimal control theory, forced hybrid mechanical systems, Riemannian and sub Riemannian metrics, geometrical optics.
Students are welcome to suggest other mathematically interesting topics in and around classical mechanics, and I will try to cover these topics in the lectures.
Knowledge of basic topics in classical mechanics, calculus of variations, differential and integral calculus, and tensor analysis is preferred.
Professor Lars Aake Andersson
讲师
安德烈·茨加诺夫
日期
2024年09月10日 至 12月26日
位置
Weekday Time Venue Online ID Password
周二,周四 09:50 - 11:25 A3-1a-205 ZOOM 01 928 682 9093 BIMSA
参考资料
[1] H. Poincare, Les Methodes Nouvelles de la Mecanique Celeste}, Tom III, Dover Pub. Inc., N.Y., (1892).
[2] E. Cartan, Lecons sur les invariants integraux, Hermann, Paris, 1922, 210 pp.
[3] P.A.M. Dirac, Generalized Hamiltonian dynamics, Can. J. Math. 2, 129 (1950).
[4] V.T. Filippov, n-Lie algebras, Siberian Math. J., 26:6 (1985), 879-891.
[5] J. Grabowski, G. Marmo, On Filippov algebroids and multiplicative Nambu-Poisson structures, Diff. Geom. Appl., 12:1, (2000), 35-50.
[6] Y. Kosmann-Schwarzbach, From Schouten to Mackenzie: Notes on brackets, J. Geom. Mech., 13:3, (2021), 459-476.
[7] H.J. Rothe and K.D. Rothe, Classical and Quantum Dynamics of Constrained Hamiltonian Systems (World Scientific, Singapore, 2010).
[8] B. Brogliato. Nonsmooth Mechanics, volume 29 of Communications and Control Engineering. Springer London, 1999.
[9] Francesco Bullo and Andrew D. Lewis. Geometric control of mechanical systems, volume 49 of Texts in Applied Mathematics. Springer-Verlag, New York, 2005.
[10] V. V. Kozlov, Dynamical systems X. General theory of vortices, Encyclopaedia Math. Sci., 67, Springer-Verlag, Berlin, 2003, 184 pp.
[11] P.J. Olver, Lectures on Moving Frames, 2011.
[12] A. A. Agrachev, Y. L. Sachkov, Control Theory from the Geometric Viewpoint, 2004
视频公开
公开
笔记公开
公开
语言
英文
讲师介绍
Andrey Tsiganov currently works at the Department of Computational Physics, Saint Petersburg State University, Russia. His main research interests are integrable and superintegrable systems in classical and quantum mechanics, nonholonomic and vakonomic mechanics, geometry and topology of dynamical systems, see profile at https://www.researchgate.net/profile/Andrey-Tsiganov. He is one of the organizers of the BIMSA Integrable System Seminar, see https://researchseminars.org/seminar/BIMSA-ISS and https://sites.google.com/view/bimsa-iss.
北京雁栖湖应用数学研究院
CONTACT

No. 544, Hefangkou Village Huaibei Town, Huairou District Beijing 101408

北京市怀柔区 河防口村544号
北京雁栖湖应用数学研究院 101408

Tel. 010-60661855
Email. administration@bimsa.cn

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