Delve into advanced classical mechanics concepts through a comprehensive series of lectures covering fundamental principles, Lagrangian and Hamiltonian formalisms, conservation laws, central forces, rigid body dynamics, special relativity, and canonical transformations. Explore virtual displacements, D'Alembert's principle, Hamilton's principle, the Lagrange multiplier method, and the Virial theorem. Examine particle orbits, the Kepler problem, scattering cross-sections, and small-scale oscillations. Study time dilation, length contraction, relativistic kinematics, and electromagnetic field tensors. Conclude with an in-depth look at Poisson brackets and Hamilton-Jacobi theory, providing a thorough understanding of classical mechanics principles and their applications.
Overview
Syllabus
01: Introduction and Fundamental principles.
02: Fundamentals part2, Generalized coordinates.
03: D´Alembert´s principle and Lagranges eq.
04: D´Alembert´s principle part 2.
05: Hamilton´s principles - Part 1.
06: Hamilton´s principles - Part 2.
07: Lagrange multiplier method - Part 1.
08: Lagrange multiplier method - Part 2.
09: Conservation laws and symmetries - Part 1.
10: Conservation laws and symmetries - Part 2.
11: Hamiltonian formalism - Part 1.
12: Hamiltonian formalism - Part 2.
13: Central forces - Part 1.
14: Central forces - Part 2.
15: Particle orbits and Virial theorem.
16: Particle orbits and Virial theorem - Part 2.
17: Kepler problem.
18: Kepler problem - Part 2.
19: Scattering cross section.
20: Scattering cross section - Part 2.
21: Rigid body rotation.
22: Rigid body rotation - Part 2.
23: Time change of vectors in rotating systems.
24: Time change of vectors in rotating systems - Part 2.
25: Rigid body motion - Part 1.
26: Rigid body motion - Part 2.
27: Gyroscope effect and spinning top.
28: Gyroscope effect and spinning top - Part 2.
30: Small-scale oscillations -- Part 2.
29: Small-scale oscillations - Part 1.
31: Normal coordinates and vibrations - Part 1.
32: Normal coordinates and vibrations - Part 2.
33: Special theory og relativity - Part 1.
34: Special theory og relativity - Part 2.
35: Lorentz transformations.
36: Lorentz transformations - Part 2.
37: Time dilation and length contraction - Part 1.
38: Time dilation and length contraction - Part 2.
39: Relativistic kinematics - Part 1.
40: Relativistic kinematics - Part 2.
41: Threshold energy - part 1.
42: Threshold energy - part 2.
43: EM field tensor and canonical transformations - Part 1.
44: EM field tensor and canonical transformations - Part 2.
45: Canonical transformations part 3.
47: Poisson brackets - Part 1.
48: Poisson brackets - Part 2.
49: April Hamilton Jacobi theory - Part 1.
50: April Hamilton Jacobi theory - Part 2.
46: Canonical transformations part 4.
51: Summary.
Taught by
NTNU Undervisning
