Birkhoffian Formulations of Bessel Equation

The Birkhoffian mechanics is more general than the Hamilton mechanics, but only some dynamical systems can be realized as a Birkhoffian formulation. This paper proposes a novel Birkhoffian formulation for the classical Bessel equation. Based on the first method of Santilli, the Birkhoffian formulation of Bessel equation is established under the assumption that the Birkhoffian describes the total physical energy of the corresponding conservative systems. Zero and n-th order classical Bessel equations are studied to verify the effectiveness of the proposed formulation.