arXiv:1310.5750v2 [math-ph] 29 Jun 2016 Hamiltonian analysis for linearly acceleration-dependent Lagrangians Miguel Cruz, 1, a) Rosario G´ omez-Cort´ es, 1 Alberto Molgado, 2, b) and Efra´ ın Rojas 1 1) Facultad de F´ ısica, Universidad Veracruzana, 91000, Xalapa, VER., M´ exico c) 2) Facultad de Ciencias, Universidad Aut´ onoma de San Luis Potos´ ı, Av. Salvador Nava S/N Zona Universitaria, CP 78290, San Luis Potos´ ı, SLP, M´ exico d) We study the constrained Ostrogradski-Hamilton framework for the equations of motion provided by mechanical systems described by second-order derivative actions with a linear dependence in the accelerations. We stress out the peculiar features provided by the surface terms arising for this type of theories and we discuss some important properties for this kind of actions in order to pave the way for the con- struction of a well defined quantum counterpart by means of canonical methods. In particular, we analyse in detail the constraint structure for these theories and its relation to the inherent conserved quantities where the associated energies together with a Noether charge may be identified. The constraint structure is fully analyzed without the introduction of auxiliary variables, as proposed in recent works involving higher order Lagrangians. Finally, we also provide some examples where our approach is explicitly applied, and emphasize the way in which our original arrangement results propitious for the Hamiltonian formulation of covariant field theories. PACS numbers: 04.20; 11.10.Ef MSC: 70H45; 70H50 Keywords: Ostrogradski; Noether; surface terms; constraints. a) On leave from: Departamento de F´ ısica, Centro de Investigaci´on y Estudios Avanzados del I.P.N., Apdo. Postal 14-740, 07000, M´ exico D.F. M´ exico b) Also at Dual CP Institute of High Energy Physics, M´ exico c) Electronic mail: miguelcruz02@uv.mx; roussjgc@gmail.com; efrojas@uv.mx d) Electronic mail: molgado@fc.uaslp.mx 1