Seminarium "The Trans-Carpathian Seminar on Geometry & Physics"

I shall present a significantly simplified version of Martinez approach to Euler-Lagrange equations on Lie algebroids. In particular no use of the "prolonged algebroids" will be made. To avoid disambiguities I shall recall fundamental constructions concerning Hamiltonian and Lagrangian formulations of the dynamics and the Euler+Lagrange equations. The Euler-Lagrange equations obtained via "Martinez method" will be compared with Euler-Lagrange equations proposed by Grabowski, Grabowska and Urbański.