13 citations · 30 across the 8 of their papers we have counts for
10 papers
Some useful operators on differential forms in Galilean and Carrollian spacetimes
Marián Fecko
Differential forms on Lorentzian spacetimes is a well-established subject. On Galilean and Carrollian spacetimes it does not seem to be quite so. This may be due to the absence of…
Galilean and Carrollian Hodge star operators
Marián Fecko
The standard Hodge star operator is naturally associated with metric tensor (and orientation). It is routinely used to concisely write down physics equations on, say, Lorentzian sp…
Vector calculus in two-dimensional space
Marián Fecko
Vector calculus in three-dimensional space is ubiquitous in applications of mathematics in physics and engineering. Its two-dimensional version is, however, quite rare. Here we try…
A generalization of vortex lines
Marian Fecko
Helmholtz theorem states that, in ideal fluid, vortex lines move with the fluid. Another Helmholtz theorem adds that strength of a vortex tube is constant along the tube. The lines…
Modern geometry in not-so-high echelons of physics: Case studies
Marian Fecko
In this mostly pedagogical tutorial article a brief introduction to modern geometrical treatment of fluid dynamics and electrodynamics is provided. The main technical tool is stand…
On symmetries and conserved quantities in Nambu mechanics
Marian Fecko
In Hamiltonian mechanics, a (continuous) symmetry leads to conserved quantity, which is a function on (extended) phase space. In Nambu mechanics, a straightforward consequence of s…
On p-form vortex-lines equations on extended phase space
Marián Fecko
In differential-geometric language, vortex-lines equations on extended phase space of a system may be written as , where is a differential 1-form. This is the s…
Gauge-potential approach to the kinematics of a moving car
Marian Fecko
A kinematics of the motion of a car is reformulated in terms of the theory of gauge potentials (connection on principal bundle). E(2)-connection originates in the no-slipping conta…
"Falling cat" connections and the momentum map
Marian Fecko
We consider a standard symplectic dynamics on TM generated by a natural Lagrangian L. The Lagrangian is assumed to be invariant with respect to the action TR_g of a Lie group G lif…
On 3+1 decompositions with respect to an observer field via differential forms
Marian Fecko
3+1 decompositions of differential forms on a Lorentzian manifold (M,g;+ - - -) with respect to arbitrary observer field and the decomposition of the standard operations acting on…