Canonical transformations are an important tool in classical mechanics, as they simplify the solution of many mechanical problems. This work first introduces the basic concepts of Lagrangian and Hamiltonian mechanics and describes the equations governing the motion of mechanical systems. The main focus is on canonical transformations, which facilitate the solving of equations of motion. We thoroughly examine generating functions and their connection to canonical transformations, as well as the mathematical properties of canonical transformations. Emphasis is also placed on the application of these transformations to specific problems. Finally, we explore Poisson brackets and canonical invariants.
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