Theoretical Mechanics 1.

Course description:
Postulates of Newtonian mechanics, the principle of the newtonian determination. Dynamical systems, existence and uniqueness of the solutions. Accelerating-rotating reference systems. The symmetries of the equations motions, first integrals, qualitative and quantitative study of one-dimensional motions, phase portraits. Oscillations. Motion in a central field. Collisions, calculation of scattering cross sections. Mechanics of point systems, first integrals and the Galilei group. The two-body-problem. Constrained motions. The principle of virtual work. The general equation of dynamics, Lagrange's equations of first and second kind. Transformations of the general coordinates. Symmetries and conservation laws, Noether's theorem. Small oscillations: normal coordinates. Hamilton's principle of the least action. General properties of the Langrange function, space-time symmetries and conservation theorems. Gauge transformation. Hamilton functions, canonical equations. Liouville's theorem. Canonical transformations. The symplectic structure of phase space, Poisson brackets. Infinitesimal canonical transformations and integrals of the motion. The Hamilton-Jacobi differential equation.

Recommended Texts:

• Goldstein H. : Classical Mechanics, Addison -Wesley, Reading 1980
• Scheck F., Mechanics, Springer, Berlin 1994
• Landau L. D., Lifshitz E. M.: Mechanics, Pergamon Press, Oxford 1976