After learning basic concepts of classical mechanics, a wierd question arises about mathematical approach to this field. The general approach goes like this differential manifold structure is associated with lagrangian and symplectic structure comes with hamiltonian. We tried to learn this, so i am attaching project report(more like a formula sheet) with topic “differential geometric treatment to hamiltonian mechanics”. Please go through this and post some views on this mathematical approach.
Classical Mechanics and Differential Geometry Friday, Feb 9 2007
Applications of Classical Physics(Caltech notes) Saturday, May 6 2006
Background: These are some immensely useful notes on many things that are not quantum. It should be useful to everyone.
These are the lecture notes for a course offered by Kip.S.Thorne at Caltech. They cover a wide range of topics in a beautiful way. I am just giving here the chapter names so that you can get an idea.
Chapter 1: Physics in Euclidean Space and Flat Spacetime: Geometric Viewpoint
Chapter 2: Kinetic Theory
Chapter 3: Statistical Mechanics
Chapter 4: Statistical Thermodynamics
Chapter5: Random Processes
Chapter6: Geometric Optics
Chapter 7: Diffraction
Chapter 8: Interference
Chapter 9: Nonlinear Optics
Chapter 10: Elastostatics
Chapter 11: Elastodynamics
Chapter 12: Foundations of Fluid Dynamics
Chapter 13: Vorticity
Chapter 14: Turbulence
Chapter 15: Waves and Rotating Flows
Chapter 15: Waves and Rotating Flows [
Chapter 16: Compressible and Supersonic Flow
Chapter 17: Convection
Chapter 18: Magnetohydrodynamics
Chapter 19: Particle Kinetics of Plasma
Chapter 20: Waves in Cold Plasmas: Two-Fluid Formalism
Chapter 21: Kinetic Theory of Warm Plasmas
Chapter 22: Nonlinear Dynamics of Plasmas
Chapter 23: From Special to General Relativity
Chapter 24: Fundamental Concepts of General Relativity
Chapter 25: Stars and Black Holes
Chapter 26: Gravitational Waves and Experimental Tests of General Relativity
Chapter 27: Cosmology
Appendix A: Concept-Based Outline of Book
Appendix B: Some Unifying Concepts
Posted by : Loganayagam.R,
Structure and Interpretation of Classical Mechanics Wednesday, Apr 19 2006
Background : I guess classical mechanics at the level of Goldstein is enough. And yeah some patience to read and understand abstract math-lingo.
The first thing – this book has some crazy notation ! Apart from that these are some good lecture notes on mathematical aspects of classical mechanics. They require some math-maturity but once you get used to all the weird looking equations and awkward conventions, it is readable. I will not recommend it for the first reading- rather read it along with somethoing else like Landau or Jose & Saletan
You can see a book review of this book that appeared in American Scientist here.
Posted by : Loganayagam.R.(Tom)