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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 .