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IPS program: TP3 (Classical Mechanics 2 and Electrodynamics 2)

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Recommended books

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T.W.B. Kibble, F.H. Berkshire: Classical Mechanics

H. Goldstein, C.P. Pole, J.L. Safko: Classical Mechanics

L.D. Landau, E.M. Lifshitz: Mechanics

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J.D. Jackson: Classical Electrodynamics

D.J. Griffiths: Introduction to Electrodynamics

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I Lagrangian Mechanics

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1 Short summary of principles in Newtonian mechanics

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1.1 Space and time

1.2 Newton's laws and some consequences

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2 Lagrangian formulation of mechanics

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2.1 Lagrange's equations - the covariant form of the equations of motion

2.2 Calculus of variations

2.3 Hamilton's principle - the principle of least action

2.4 Some first examples

2.5 Extensions of Hamilton's principle to non-conservative and non-holonomic systems

2.6 Examples

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3 Conservation laws in Lagrangian mechanics

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3.1 Cyclic coordinates, definition of energy

3.2 Behavior of the Lagrangian under transformations of generalized coordinates and time

3.3 The Noether's theorem

3.4 Conservation laws for isolated systems

3.5 Motion of a rocket

3.6 Motion in non-inertial frames in Lagrangian mechanics

3.7 Two-body problem

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II Hamiltonian Mechanics

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4 Hamiltonian formulation of mechanics

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4.1 Hamilton's equations - the canonical equations of motion

4.2 Variational principle for Hamilton's equations

4.3 Poisson brackets

4.4 Canonical transformations

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5 Hamilton-Jacobi Theory

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5.1 The action as function of coordinates and time

5.2 Hamilton-Jacobi equation

5.3 Separation of variables

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III Electrodynamics of time-varying fields and special relativity

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6 Maxwell equations

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6.1 Summary on Maxwell equations

6.2 Vector and scalar potential

6.3 Energy and momentum conservation in electrodynamics

6.4 Transformation properties of physical quantities
under rotations, spatial reflections and time reversal

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7 Plane electromagnetic waves and wave propagation

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7.1 Plane waves in a nonconducting medium

7.2 Linear and circular polarization, Stokes parameters

7.3 Reflection and refraction of electromagnetic waves at a plane interface
between dielectrics

7.4 Superposition of waves in one dimension

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8. Radiating systems

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8.1 Fields and radiation of a localized oscillating source

8.2 Electric dipole fields and radiation

8.3 Magnetic dipole and electric quadrupole fields

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9 Special theory of relativity

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9.1 Einstein's two postulates

9.2 Lorentz transformation and basic kinematic results of special relativity

9.3 Addition of velocities, 4-velocity

9.4 Relativistic momentum and energy of a particle

9.5 Mathematical properties of the space-time of special relativity

9.6 Matrix representation of the Lorentz transformation, infinitesimal generators

9.7 Covariance of electrodynamics

9.8 Lorentz transformations of electromagnetic fields

9.9 Lagrangian for
relativistic particles in external electromagnetic fields (Elementary approach)

9.10 Lagrangian for the electromagnetic field

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Last update: July, 2017