3 citations · 5 across the 5 of their papers we have counts for
10 papers
Homogenous Lagrangian systems
Wlodzimierz M. Tulczyjew, Pawel Urbanski
The application of the Legendre transformation to a hyperregular Lagrangian system results in a Hamiltonian vector field generated by a Hamiltonian defined on the phase space of th…
Frame-independent formulation of Newtonian mechanics
Katarzyna Grabowska, Pawel Urbanski
A frame independent formulation of analytical mechanics in the Newtonian space-time is presented. The differential geometry of affine values i.e., the differential geometry in whic…
An affine framework for analytical mechanics
Pawel Urbanski
An affine Cartan calculus is developed. The concepts of special affine bundles and special affine duality are introduced. The canonical isomorphisms, fundamental for Lagrangian and…
Jacobi structures on affine bundles
J. Grabowski, D. Iglesias, J. C. Marrero +2
We study affine Jacobi structures on an affine bundle , i.e. Jacobi brackets that close on affine functions. We prove that there is a one-to-one correspondence between af…
On characterization of Poisson and Jacobi structures
Janusz Grabowski, Pawel Urbanski
We characterize Poisson and Jacobi structures by means of complete lifts of the corresponding tensors: the lifts have to be related to canonical structures by morphisms of correspo…
Lie brackets on affine bundles
Janusz Grabowski, Katarzyna Grabowska, Pawel Urbanski
Natural analogs of Lie brackets on affine bundles are studied, based on natural examples from differential geometry and analytical mechanics. In particular, a close relation to Lie…