F5510 Analytical Mechanics

Exercises: Wednesdays 08:00-09:00.
Lectures : Wednesdays 09:00-11:00.

Both lectures and exercises take place in F4, 3rd floor, building 6.

Course Plan, Fall 2026:

Wednesday 16.09.26 at 08:00
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;

Wednesday 23.09.26
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;
Exercises: Handout: Two pendulum problems;

Wednesday 30.09.26
Gen. Potential for Fictitious Forces [LL1] 39;
Lagrange Eqs. with Semi-Holonomic Constraints [G3] 2.4;

Wednesday 07.10.26
Variational Derivative, Principle of Stationary/Least Action [G3] 2.1-2.3;
Dictionary between Point Mechanics and Field Theory;
Exercises: [G3] 2.18 + 2.20;

Wednesday 14.10.26
Total derivative terms;
Noether's Theorem, Symmetry, Local vs. Global, Conservation Law, On-shell vs. Off-shell [KB] [G3] 13.7;
Exercises: [G3] 2.3 + 2.12;

Wednesday 21.10.26
From Discrete to Continuous Indices, Longitudinal Motion in Wire [G3] 13.1;
Special Relativistic Version of "Kinetic Term" T [LL2] 8;
Exercises: Handout: Maxwell Eqs. from Action Principle;

Wednesday 28.10.26
Czech Holiday. No lectures.

Wednesday 04.11.26
Test/quiz; Exercises: Handout: Geodesic Equation [LL2] 86-87;

Wednesday 11.11.26

Wednesday 18.11.26

Wednesday 25.11.26

Wednesday 02.12.26

Wednesday 09.12.26

Wednesday 16.12.26

Course Material:

[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.
[M]: P. Mann, "Lagrangian and Hamiltonian dynamics", 2018.
[SWM]: G.J. Sussman and J. Wisdom with M.E. Mayer, "Structure and Interpretation of Classical Mechanics", html .