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F5510 Analytical Mechanics
Exercises: Wednesdays 14:00-15:00.
Lectures : Wednesdays 15:00-17:00.
Both lectures and exercises take place in FLenc, 3rd floor, building 6.
Course Plan, Fall 2024:
Wednesday 18.09.24 at 14:00
Cancelled due to floods.
Wednesday 25.09.24
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 02.10.24
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 09.10.24
Gen. Potential for Fictitious Forces [LL1] 39;
Lagrange Eqs. with Semi-Holonomic Constraints [G3] 2.4;
Variational Derivative, Principle of Stationary/Least Action [G3] 2.1-2.3;
Wednesday 16.10.24
Dictionary between Point Mechanics and Field Theory;
Total derivative terms;
Tensors, scalars, vectors, co-verctors & indices;
Exercises: [G3] 2.18 + 2.20;
Wednesday 23.10.24
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 30.10.24
Special Relativistic Version of "Kinetic Term" T [LL2] 8;
Total action for E&M;
Exercises: Handout: Maxwell Eqs. from Action Principle;
Wednesday 06.11.24
From Discrete to Continuous Indices,
Longitudinal Motion in Wire [G3] 13.1;
Exercises: Handout: Geodesic Equation [LL2] 86-87;
Wednesday 13.11.24
Legendre Transformation, Hamilton's Equations [G3] 8.1-8.2, 8.5 [LL1] 40;
Symplectic Notation [G3] 9.4;
Poisson Bracket (PB) [G3] 9.4 [LL1] 42;
Classical Mechanics vs. Quantum Mechanics,
Hamilton's EOM vs. Heisenberg EOM [G3] 9.5;
Exercises: [G3] 13.1;
Wednesday 20.11.24
Constants of motion, Poisson's Theorem [G3] 9.6 [LL1] 42;
Extended Canonical Transformations (CT),
The Four Archetypes of CT [G3] 9.1 [LL1] 45;
Exercises: [G3] 8.23 + 8.28;
Wednesday 27.11.24
Exercises: [G3] 8.2;
Wednesday 04.12.24
Wednesday 11.12.24
Wednesday 18.12.24
Last lecture.
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 .