Foundations of Mechanics

TL;DR: In this article, the authors studied discrete second-order vakonomic mechanics, that is, constrained variational problems for secondorder lagrangian systems, and derived geometric integrators which are symplectic and preserve the momentum map.

TL;DR: For weak non-conservative systems, whose dynamical equations admit adjoint symmetries, there exist Poincare and Cartan integral invariants on an extended phase space as discussed by the authors.

TL;DR: In this paper, it was shown that one can obtain an sh-Lie algebra where the only non-zero mappings defining it are the lower order mappings, and that the graded space can be replaced by another graded space, with only three nonzero terms.

TL;DR: In this paper, a detailed analytical description of the global dynamics of a point mass moving on a sphere under the action of a logarithmic potential is given, and a McGehee-type blow-up is performed in order to cope with the singularity of the potential when the point mass goes through a singularity.