Title Lie Algebroid in Classical Mechanical and Optimal Control Type of Research Presentation Keywords Lie algebroid, lagrangian mechanics, variational calculuse,reduction of dynamical systems, optimal control system Abstract In this paper, we consider the symplectic and variational formalism and we study reduction, we also consider optimal control system on lie algebroid and show how to reduce Pontryagin maximum principale Researchers Ghorbanali Haghighatdoost Bonab (First Researcher)، (Second Researcher)