这大概是目前网上最好的哈密顿力学课。2020年Univ of virginia的课，优Shane Ross上。但是视频只有一半，后一半，前一半是线下上的，暂时只有课件。前一半的视频Ross一直说要补上，原话见
https://www.youtube.com/watch?v=z-dGZgq-6jg&list=PLUeHTafWecAVCauQ541UBrfGqHQwuHq_2&index=2&t=1s下面的Ross回复，看上半年能不能补上。如果补全了，这必然是目前最好的哈密顿力学课。
Ross是Jerrold Marsden的学生，他这个人还有一个好处，颇有网红潜质，发twitter频率很高，当然都是学术相关。他自己的YouTube视频下面也有很多回复。
下面是课程介绍，包括视频，课件……
https://www.youtube.com/playlist?list=PLUeHTafWecAVCauQ541UBrfGqHQwuHq_2
Advanced dynamics - Hamiltonian systems and nonlinear dynamics
13 videos1,731 viewsUpdated 6 days ago
By Dr. Shane Ross of Virginia Tech's Department of Aerospace and Ocean Engineering.
This course gives the student advanced theoretical and semi-analytical tools for analysis of dynamical systems, particularly mechanical systems (e.g., particles, rigid bodies, continuum systems). We discuss methods for writing equations of motion and the mathematical structure they represent at a more sophisticated level than previous engineering dynamics courses. We consider the sets of possible motion of mechanical systems (trajectories in phase space), which leads to topics of Hamiltonian systems (canonical and non-canonical), nonlinear dynamics, periodic and quasi-periodic orbits, driven nonlinear oscillators, resonance, stability / instability, invariant manifolds, energy surfaces, chaos, Poisson brackets, basins of attraction, etc.
The entire class notes are in OneNote form:
https://www.youtube.com/redirect?event=playlist_description&redir_token=QUFFLUhqbGdxRGgzV2t6RDFjYkNCUFJxSkZ1Zmw0V0tfZ3xBQ3Jtc0tuMG1pdmZ1NXdkcm1XYk92ektkUWhEaWYtVlZhNHV2X1NDdXJaaGo3eWUxOTg4ek1RalRSb2xWYWFtSGNlblVleUJaMXBNT1UxTkFBTjl6b3hDTm5rWEpNQUNSeUJlSG9jTUh1d1hZaGd2bzJSdzU5UQ&q=https%3A%2F%2F1drv.ms%2Fu%2Fs%21ApKh50Sn6rEDiRgCYBrjscAYJDUk%3Fe%3DIE5wnQ
and in PDF form:
https://www.youtube.com/redirect?event=playlist_description&redir_token=QUFFLUhqbGZCRWpubmVOUVMtM1p0aVFIR1k1YzhXNEZ5UXxBQ3Jtc0tscUFCaWFOcjRBdW9qeW0xMWVSVGFUZi1tM21HWVFXT2J5M1VzSm9ZRGVjVXB3NVdySzhXbk5DcDlZRVVMbENIU09BQ2VLeTItd0tRb3RvUU1oc2d0TmxHRkZnazNhSk5fcGNNM1pULXVpdzlNZEU5UQ&q=https%3A%2F%2Fdrive.google.com%2Fdrive%2Ffolders%2F1Itc4hCCYWS48piSpYGtE6KcWj5CGtGQe%3Fusp%3Dsharing
The video lectures start halfway through the course (due to the Covid-19 pandemic), but the lecture notes above go back to the beginning.This course builds on prior knowledge of Lagrangian and rigid body mechanics, which have their own lecture series:
https://is.gd/AnalyticalDynamics
This course builds on prior knowledge of Lagrangian and rigid body mechanics, which have their own lecture series:
https://is.gd/AnalyticalDynamicsThere is a continuation of this course on a related topic, Center manifolds, normal forms, and bifurcations, available here:
https://is.gd/CenterManifolds
If you want a simple introductory course on Nonlinear Dynamics and Chaos, see:
https://is.gd/NonlinearDynamics
※ 修改:·vinbo 于 Jul 7 15:21:56 2022 修改本文·[FROM: 211.161.249.*]
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