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F5510 Analytical Mechanics


My skype handle is: klaus_bering. Join F5510 skype group.

Exercises: Wednesdays 10:00-11:00.
Lectures : Wednesdays 11:00-13:00.

Both lectures and exercises take place online at Google classroom .
Meeting Nickname: epcdxgot4b . Class code: 4itk46w .

NB: At your IS External Services G Suite should be enabled. Especially you need IS to generate a Google Mail account via your UCO number.

Videos of lectures are uploaded to IS .

Course Plan, Fall 2020:


Wednesday 07.10.20
Holonomic, Semi-Holonomic & Non-Holonomic Constraints [G3] 1.3;
Principle of Virtual Work, D'Alembert's Principle, From Newton's to Lagrange's Eqs. [G3] 1.4;
Applications, Atwood's Machine [G3] 1.6; (video)

Wednesday 14.10.20
Gen. Potential for Lorentz Force [G3] 1.5;
Friction Forces, Rayleigh's Dissipative Function [G3] 1.5;
Canonical Momentum, Energy Function, Energy Conservation [G3] 2.6;
Virial Theorem [G3] 3.4; (video)

Wednesday 21.10.20
Gen. Potential for Fictitious Forces [LL1] 39;
Lagrange Eqs. with Semi-Holonomic Constraints [G3] 2.4;
Virial Theorem [G3] 3.4;
Exercises: Handout: Two pendulum problems; (video)

Wednesday 28.10.20
Dictionary between Point Mechanics and Field Theory;
Variational Derivative, Principle of Stationary/Least Action [G3] 2.1-2.3;
Exercises: [G3] 2.18 + 2.20; (video)

Wednesday 04.11.20
Exercises: [G3] 2.3 + 2.12;

Wednesday 11.11.20

Wednesday 18.11.20

Wednesday 25.11.20

References:

[G2]: Herbert Goldstein, "Classical Mechanics", Eds. 2.
[G3]: Herbert Goldstein, "Classical Mechanics", Eds. 3. (Click here for a list of corrections).
[LL1]: Landau and Lifshitz, Vol. 1, "Mechanics".
[LL2]: Landau and Lifshitz, Vol. 2, "The Classical Theory of Fields".
[KB]: Klaus Bering, "Noether's Theorem for a Fixed Region", arXiv:0911.0169 .

Nota Bene:

1. All references to [LL2] should be considered supplementary reading, as the presentation during the lectures differs substantially.
2. What Goldstein [G3] calls "Hamilton's principle" is usually called the "principle of stationary/least action".
3. What Goldstein [G3] calls "principle of least action" [G3] 8.6, is usually called the "principle of abbreviated action" or "Maupertuis' principle".
4. Note that Poisson brackets in [LL1] have the opposite sign convention.
5. The treatment of Lagrange equations for semi-holonomic & non-holonomic constraints in [G3] 2.4 is inconsistent with Newton's laws, and has been retracted on [G3]'s errata homepage . For more info, see also M.R. Flannery, "The enigma of nonholonomic constraints", Am. J. Phys. 73 (2005) 265 .

Supplementary References:

[JS]: J.V. Jose and E.J. Saletan, "Classical Dynamics: A Contemporary Approach", 1998.
[L]: N.A. Lemos, "Analytical Mechanics", 2018.
[SWM]: G.J. Sussman and J. Wisdom with M.E. Mayer, "Structure and Interpretation of Classical Mechanics", html .