An alternate Hamiltonian H different from Ostrogradski’s one is found for the Lagrangian L = L(q, q̇, q̈), where ∂2L/∂(q̈)2 6= 0. We add a suitable divergence to L and insert a = q an d b = q̈. Contrary to other approaches no constraint is needed because ä = b is one of the canonical equations. Another canonical equation becomes equivalent to the fourth–order Euler–Lagrange equation of L. Usually, ...

This article is concerned with the fourth-order compact scheme for an accurate simulation of acoustic waves in the frequency domain. The compact schemes are known for a long time; however, they have shown diÆculties, in particular, in dealing with general boundary conditions. This article introduces a new formulation for the compact scheme for the Helmholtz equation and an e ective strategy of ...

The conformal equivalence of fourth–order gravity following from a non–linear Lagrangian L(R) to theories of other types is widely known, here we report on a new conformal equivalence of these theories to theories of the same type but with different Lagrangian. For a quantization of fourth-order theories one needs a Hamiltonian formulation of them. One of the possibilities to do so goes back to...