The Journal of Geometric Mechanics: latest papers Latest articles for selected journal Second-order constrained variational problems on Lie algebroids: Applications to optimal control Leonardo Colombo Wed, 1 Mar 2017 08:00:00 GMT Covariant Hamiltonian field theories on manifolds with boundary: Yang-Mills theories     It is also shown that the natural interpretation of the Euler-Lagrange equations as an evolution system near the boundary leads to a presymplectic Hamiltonian system in an extended phase space containing the natural configuration and momenta fields at the boundary together with extra degrees of freedom corresponding to the transversal components at the boundary of the momenta fields of the theory. The consistency conditions for evolution at the boundary are analyzed and the reduced phase space of the system is shown to be a symplectic manifold with a distinguished isotropic submanifold corresponding to the boundary data of the solutions of Euler-Lagrange equations. This setting makes it possible to define well-posed boundary conditions, and provides the adequate setting for the canonical quantization of the system.
    The notions of the theory are tested against three significant examples: scalar fields, Poisson $\sigma$-model and Yang-Mills theories. ]]>
Alberto Ibort and Amelia Spivak Wed, 1 Mar 2017 08:00:00 GMT The $2$-plectic structures induced by the Lie bialgebras Mohammad Shafiee Wed, 1 Mar 2017 08:00:00 GMT Uniform motions in central fields Martin Swaczyna and Petr Volný Wed, 1 Mar 2017 08:00:00 GMT