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 …
Hamiltonian and Lagrangian formalisms which serves for contact manifolds. The role of the …
[HTML][HTML] Dirac algebroids in Lagrangian and Hamiltonian mechanics
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 …
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 …
describing mechanical systems, even those with singular Lagrangians or subject to …
Tulczyjew triples in higher derivative field theory
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 …
analytical mechanics and first order field theory to describe a wide range of physical systems …
[HTML][HTML] AV-differential geometry: Euler–Lagrange equations
A general, consistent and complete framework for geometrical formulation of mechanical
systems is proposed, based on certain structures on affine bundles (affgebroids) that …
systems is proposed, based on certain structures on affine bundles (affgebroids) that …
[PDF][PDF] Reduction of symplectic principal R-bundles
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 …
momentum map. This type of structures plays an important role in the geometric formulation …
The Schrödinger operator as a generalized Laplacian
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 …
them independent of the class of inertial observers. In this picture the Schrödinger operators …
The Schrödinger operator in Newtonian space-time
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 …
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 …
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 …
Lagragian system whose Lagrangian is a section of an AV-bundle Z1 over the evolution …