Gauge transformations in dynamical systems of finite dimension

Summary

 0. Introduction
 1. Lagrangian formalism
 2. Hamiltonian formalism
 3. Stabilization in hamiltonian formalism
 4. Non-uniqueness of solutions in hamiltonian formalism
 5. Hamiltonian dynamical symmetry transformations
 6. Stabilization in lagrangian formalism
 7. Lagrangian dynamical symmetry transformations
 8. Gauge fixing, degrees of freedom
 9. Extensions of the formalism
10. Conclusions
Example 1. Classical mechanics
Example 2. Reparametrizations
Example 3. Free relativistic particle
Example 4. The DGL model
Example 5. 
Appendix A. Some constructions with vector bundles
Appendix B. Submanifolds
Appendix C. Projectability of functions and vector fields
Appendix D. Canonical structures of the tangent bundle
Appendix E. Canonical structures of the cotangent bundle
Appendix F. Differential equations on a manifold
Appendix G. Proof of equation (4.13)
Bibliography