A Complete Course on Theoretical Physics pp 55-162 | Cite as

# Classical Mechanics

## Abstract

In addition to the standard examples treated with Newtonian and Lagrangian mechanics, the highlights of this chapter are (Newtonian and Stokesian) friction, velocity-dependent forces, (gauge) transformations and generating functions, dissipation, phase space considerations, the mathematical pendulum (with elliptic integrals), oscillations (with Laplace transform and Green functions), the time-shift matrix (Floquet operator), stability of solutions (including Lyapunov exponents), Matthieu’s and Hill’s differential equations, Matthieu functions, and parametric resonance. Hamilton mechanics, canonical transformations, the Liouville equation, and the Hamilton–Jacobi theory are introduced along with the notion of arbitrary “coordinates” in phase space. Reference is often made to the limited phase space elements required by quantum theory. There is a list of 48 problems.

## Supplementary material

## References

- 1.M. Abramowitz, I.A. Stegun,
*Handbook of Mathematical Functions*(Dover, New York, 1970)zbMATHGoogle Scholar - 2.P.F. Byrd, M.D. Friedman,
*Handbook of Elliptic Integrals for Engineers and Physicists*(Springer, Berlin, 1954)CrossRefGoogle Scholar - 3.J. Meixner, F.W. Schäfke, G. Wolf,
*Mathieu Functions and Spheroidal Functions and Their Mathematical Foundations*(Springer, Berlin, 1980)CrossRefGoogle Scholar - 4.D.H. Kobe, K.H. Yang, Eur. J. Phys.
**80**, 236 (1987)CrossRefGoogle Scholar - 5.A. Lindner, H. Freese, J. Phys. A
**27**, 5565 (1994)ADSMathSciNetCrossRefGoogle Scholar

## Suggestions for Textbooks and Further Reading

- 6.W. Greiner,
*Classical Mechanics—System of Particles and Hamiltonian Dynamics*(Springer, New York, 2010)Google Scholar - 7.L.D. Landau, E.M. Lifshitz,
*Course of Theoretical Physics. Volume 1—Mechanics*, 3rd edn. (Butterworth-Heinemann, Oxford, 1976)Google Scholar - 8.W. Nolting,
*Theoretical Physics 1—Classical Mechanics*(Springer, Berlin, 2016)Google Scholar - 9.W. Nolting,
*Theoretical Physics 2—Analytical Mechanics*(Springer, Berlin, 2016)CrossRefGoogle Scholar - 10.F. Scheck,
*Mechanics—From Newton’s Laws to Deterministic Chaos*(Springer, Berlin, 2010)Google Scholar - 11.A. Sommerfeld,
*Lectures on Theoretical Physics 1—Mechanics*(Academic, London, 1964)Google Scholar - 12.D. Strauch,
*Classical Mechanics*(Springer, Berlin, 2009)CrossRefGoogle Scholar - 13.W. Thirring,
*Classical Mathematical Physics: Dynamical Systems and Field Theories*, 3rd edn. (Springer, New York, 2013)Google Scholar - 14.G. Ludwig,
*Einführung in die Grundlagen der Theoretischen Physik 1–4*(Vieweg, Braunschweig, 1974) (in German)Google Scholar - 15.M. Mizushima,
*Theoretical Physics: From Classical Mechanics to Group Theory of Microparticles*(Wiley, New York, 1972)Google Scholar