2005/11/21 by Alfredo Takashi Suzuki, Suzuki, A. T., Jorge Sales +1
Engineering · Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Control and Stability of Dynamical Systems #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.hep-th/0511211
openalex publication_date 2005/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In classical mechanics, we can describe the dynamics of a given system using either the Lagrangian formalism or the Hamiltonian formalism, the choice of either one being determined by whether one wants to deal with a second degree differential equation or a pair of first degree ones. For the former approach, we know that the Euler-Lagrange equation of motion remains invariant under additive total derivative with respect to time of any function of coordinates and time in the Lagrangian function, whereas the latter one is invariant under canonical transformations. In this short paper we address the question whether the transformation that leaves the Euler-Lagrange equation of motion invariant is also a canonical transformation and show that it is not.