In the present work, we seek to obtain the equations of motion for the oblique launch of a small sphere without undergoing rotation subject to air resistance through the lagrangian and hamiltonian formalisms for dissipative systems. To this end, we reviewed the Newtonian, Lagrangian and Hamiltonian formalisms of classical mechanics for conservative systems, as these serve as the basis for the Lagrangian and Hamiltonian formulations for dissipative systems. In addition, we made a brief discussion about fractional calculus, where we made a brief historical approach to this branch of mathematics, then highlighted the fractional calculus promoted by Riemann-Liouville and Caputo, considering that these calculations were used in the method of lagrangian dependent on fractional derivatives, which is one of the methods used to obtain the equations of motion. Finally, we found the equations of motion we were looking for through the lagrangian and hamiltonian formalisms for dissipative systems using the Rayleigh dissipation function, the equivalent lagrangian function and the fractional derivative dependent lagrangian method.
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