130 citations · 467 across the 26 of their papers we have counts for
28 papers
New developments in geometric mechanics
A. J. Bruce, K. Grabowska, J. Grabowski +1
We review the concept of a graded bundle, which is a generalisation of a vector bundle, its linearisation, and a double structure of this kind. We then present applications of thes…
Tulczyjew triples in the constrained dynamics of strings
Janusz Grabowski, Katarzyna Grabowska, Pawel Urbanski
We show that there exists a natural Tulczyjew triple in the dynamics of objects for which the standard kinematic configuration space , i.e. the tangent bundle, is replaced with…
Geometry of Lagrangian and Hamiltonian formalisms in the dynamics of strings
Katarzyna Grabowska, Janusz Grabowski, Pawel Urbanski
The Lagrangian description of mechanical systems and the Legendre Transformation (considered as a passage from the Lagrangian to the Hamiltonian formulation of the dynamics) for po…
Regularity of generating families of functions
Wlodzimierz M. Tulczyjew, Pawel Urbanski
We describe the geometric structures involved in the variational formulation of physical theories. In presence of these structures, the constitutive set of a physical system can be…
Double Affine Bundles
Janusz Grabowski, Mikolaj Rotkiewicz, Pawel Urbanski
A theory of double affine and special double affine bundles, i.e. differential manifolds with two compatible (special) affine bundle structures, is developed as an affine counterpa…
Liouville structures
W. M. Tulczyjew, P. Urbanski
A 'Liouville structure' is a structure isomorphic to a cotangent vector fibration. A Liouville structure is an essential ingredient of every variational formulation of a physical t…