| Center |
| Student Information Service-Master |
| Departament |
| Theoretical Physics |
| Lecturers in charge |
| Sin datos cargados |
| Met. Docent |
| Written exam with theory questions and problems. |
| Met. Avaluació |
| - - |
| Bibliografia |
| C. Gignoux y B. Silvestre-Brac, Mécanique, EDP Sciencies, Universite Joseph Fourier, Grenoble, 2002 L. N. Hand y J. D. Finch, Analytical Mechanics, Cambridge University Press, 1998 H. Goldstein, ``Clasisical Mechanics , Addison-Wesley Publishing Company, 1980 F. Scheck, ``Mechanics , Springer-Verlag, 1990 I. Percival y D. Richards, ``Introduction to Dynamics , Cambridge University Press 1982 E. C. G. Sudarshan y N. Mukunda, ``Classical Dynamics: A Modern Perspective , Jhon Wiley & Sons 1974 E. J. Saletan y A. H. Cromer, ``Theoretical Mechanics , Jhon Wiley & Sons, 1971 A. Rañada, "Diámica Clásica", Alianza Universidad Textos, 1994 |
| Continguts |
| I. Principle of Hamilton. Euler-Lagrange Equations 1. - Newton and Euler-Lagrange equations. 2. - Hamilton variational principle. Functional derivative. 3. - Links and D Alembert principle. 4. - Maupertuis variational principle. 5. - Degenerate Lagrangians. II. Symmetries and Motion Constants. 1. - Motion constant. 2. - Symmetries and conservation laws. Theorem of Noether. Examples. 3. - Lie algebra of symmetry transformations. 4. - Relativistic systems. 5. - "Gauge" symmetries. III. Hamilton Equations and Canonical Formalism. 1. - Legendre transformation and Hamilton canonical equations. 2. - Phasic space. First integrals and Poisson parenthesis. 3. - Simplectic structure of the phasic space. 4. - Canonical transformations. 5. - Poincaré - Cartan invariable integral. Liouville theorem. 6. - Symmetries in the phasic space. 7. - Generating functions. 8. - Hamilton - Jacobi equation. Hamilton principal function. 9. - Transition to Quantum Mechanics. IV. Integrability 1. - Integrable systems. Liouville theorem. 2. - Global aspects: theorem of Arnold. Invariable toroids. 3. - Action - angle variable. 4. û Super-integrable systems. Degeneration. 5. û Semi-classic rules of quantizing. 6. û Poincaré application and section surfaces. 7. - Non integrable systems. Transition to Ch |