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The integrable systems known as "AKS systems" admit a natural formulation interms of a Hamiltonian picture. The Lagrangian side of these systems are farless known; a version in these terms can be found in a work of Feher et al. Thepurpose of these notes in to provide a novel description of AKS systems interms of a variational problem different from the usual in mechanics.Additionally, and using techniques borrowed from an article of M. Gotay, it waspossible to build the Hamiltonian side of this variational problem, allowing usto establish the equivalence with the usual approach to these integrablesystems.

AKS systems and Lepage equivalent problems