Contact geometric mechanics: the Tulczyjew triples

K Grabowska, J Grabowski - arxiv preprint arxiv:2209.03154, 2022 - arxiv.org
We propose a generalization of the classical Tulczyjew triple as a geometric tool in
Hamiltonian and Lagrangian formalisms which serves for contact manifolds. The role of the …

[HTML][HTML] Dirac algebroids in Lagrangian and Hamiltonian mechanics

K Grabowska, J Grabowski - Journal of Geometry and Physics, 2011 - Elsevier
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 …

A Tulczyjew triple for classical fields

K Grabowska - Journal of Physics A: Mathematical and …, 2012 - iopscience.iop.org
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 …

Tulczyjew triples in higher derivative field theory

K Grabowska, L Vitagliano - arxiv preprint arxiv:1406.6503, 2014 - arxiv.org
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 …

[HTML][HTML] AV-differential geometry: Euler–Lagrange equations

K Grabowska, J Grabowski, P Urbański - Journal of Geometry and Physics, 2007 - Elsevier
A general, consistent and complete framework for geometrical formulation of mechanical
systems is proposed, based on certain structures on affine bundles (affgebroids) that …

[PDF][PDF] Reduction of symplectic principal R-bundles

I Lacirasella, JC Marrero, E Padrón - J. Phys. A, 2012 - researchgate.net
We describe a reduction process for symplectic principal R-bundles in the presence of a
momentum map. This type of structures plays an important role in the geometric formulation …

The Schrödinger operator as a generalized Laplacian

K Grabowska, J Grabowski… - Journal of Physics A …, 2008 - iopscience.iop.org
The Schrödinger operators on the Newtonian spacetime are defined in a way which make
them independent of the class of inertial observers. In this picture the Schrödinger operators …

The Schrödinger operator in Newtonian space-time

K Grabowska, J Grabowski, P Urbański - arxiv preprint math-ph/0611044, 2006 - arxiv.org
The Schroedinger operator on the Newtonian space-time is defined in a way which is
independent on the class of inertial observers. In this picture the Schroedinger operator acts …

AV-differential geometry and calculus of variations

K Grabowska, P Urbanski - arxiv preprint math-ph/0612069, 2006 - arxiv.org
arxiv:math-ph/0612069v1 20 Dec 2006 AV-differential geometry and calculus of variations
Page 1 arxiv:math-ph/0612069v1 20 Dec 2006 AV-differential geometry and calculus of …

[PDF][PDF] AV-bundles, Lie algebroid theory and the inhomogeneous cosymplectic formulation of the dynamics in jet manifolds

JC Marrero - Preprint. cf. MR 2008c - Citeseer
In this paper, we develop a cosymplectic inhomogeneous formulation for a (regular)
Lagragian system whose Lagrangian is a section of an AV-bundle Z1 over the evolution …