Variational calculus on a vector bundle E equipped with a structure of a general algebroid is
developed, together with the corresponding analogs of Euler–Lagrange equations …

Lie algebras are extended to the affine case using the heap operation, giving them a
definition that is not dependent on the unique element 0, such that they still adhere to …

We present a unified approach to constrained implicit Lagrangian and Hamiltonian systems
based on the introduced concept of Dirac algebroid. The latter is a certain almost Dirac …

In this paper we develop a geometric approach to higher order mechanics on graded
bundles in both, the Lagrangian and Hamiltonian formalism, via the recently discovered …

All semidirect product and functorial trivializations of first order and iterated bundles over a
Lie group are presented. For cotangent bundles, symplectic reduction is applied to obtain …

The geometrical structure known as the Tulczyjew triple has proved to be very useful in
describing mechanical systems, even those with singular Lagrangians or subject to …

The geometrical structure known as Tulczyjew triple has been used with success in
analytical mechanics and first order field theory to describe a wide range of physical systems …

It has been a long standing question how to extend, in the finite-dimensional setting, the
canonical Poisson bracket formulation from classical mechanics to classical field theories, in …

A description of classical field theories of first order in terms of Lagrangian submanifolds of
premultisymplectic manifolds is presented. For this purpose, a Tulczyjew's triple associated …

A description of time-dependent mechanics in terms of Lagrangian submanifolds of
presymplectic and Poisson manifolds is presented. Two new Tulczyjew triples are …