Related papers: Covariant Time Derivatives for Dynamical Systems
Time-dependent structures often appear in differential geometry, particularly in the study of non-autonomous differential equations on manifolds. One may study the geodesics associated with a time-dependent Riemannian metric by extremizing…
A four dimensional treatment of nonrelativistic space-time gives a natural frame to deal with objective time derivatives. In this framework some well known objective time derivatives of continuum mechanics appear as Lie-derivatives. Their…
To understand the coupling behavior of the spinor with spacetime, the explicit form of the energy-momentum tensor of the spinor in curved spacetime is important. This problem seems to be overlooked for a long time. In this paper we derive…
Observer-invariance is regarded as a minimum requirement for an appropriate definition of time derivatives. We systematically discuss such time derivatives for surface tensor field and provide explicit formulations for material,…
We present detailed pedagogical derivation of covariant derivative of fermions and some related expressions, including commutator of covariant derivatives and energy-momentum tensor of a free Dirac field. On top of that, local conformal…
The covariant derivative capable of differentiating and parallel transporting tangent vectors and other geometric objects induced by a parameter-dependent quantum state is introduced. It is proved to be covariant under gauge and coordinate…
A covariant algorithm for deriving the conserved quantities for natural Hamiltonian systems is combined with the non-relativistic framework of Eisenhart, and of Duval, in which the classical trajectories arise as geodesics in a higher…
We present a direct derivation of the typical time derivatives used in a continuum description of complex fluid flows, harnessing the principles of the kinematics of line elements. The evolution of the microstructural conformation tensor in…
A possibility to represent the standard model of fundamental particles covariant derivatives by means of approximate generalized fractional Riemann-Liouville derivatives of multifractal time and space model is shown.
I present a covariant approach to developing 1+3 formalism without an introduction of any basis or coordinates. In the formalism, a spacetime which has a timelike congruence is assumed. Then, tensors are split into temporal and spatial…
A general dynamical invariant operator for three coupled time-dependent oscillators is derived. Although the obtained invariant operator satisfies the Liouville-von Neumann equation, its mathematical formula is somewhat complicated due to…
Derivatives of equations of motion describing the rigid body dynamics are becoming increasingly relevant for the robotics community and find many applications in design and control of robotic systems. Controlling robots, and multibody…
It is developed the considerations from (S. M. Min\v{c}i\'c, [14, 15]) about curvature tensors and pseudotensors for a non-symmetric affine connection space in this paper. How many kinds of covariant derivatives are enough to be defined for…
It is shown that linear time-dependent invariants for arbitrary multi\-dimensional quadratic systems can be obtained from the Lagrangian and Hamiltonian formulation procedures by considering a variation of coordinates and momenta that…
The slightly subtle notion of covariant Lie derivatives of \textit{bundle-valued} differential forms is crucial in many applications in physics, notably in the computation of conserved currents in gauge theories, and yet the literature on…
A model is proposed, according to which the metric tensor field in the standard gravitational Lagrangian is decomposed into a projection (generally - with a non-zero covariant derivative) tensor field, orthogonal to an arbitrary 4-vector…
Recently, some problems have been found in the definition of the partial derivative in the case of the presence of both explicit and implicit functional dependencies in the classical analysis. In this talk we investigate the influence of…
We investigate stress-energy tensors constructed from the covariant derivatives of delta functions on a worldline. Since covariant derivatives are used all the components transform as tensors. We derive the dynamical equations for the…
The one loop UV divergences of Hilbert-Einstein gravity with a cosmological constant and spin 0, 1/2 and 1 matter are computed making use of a covariant derivative expansion and functional methods. For this purpose the transformation that…
Standard practice attempts to remove coordinate influence in physics through the use of invariant equations. Trans-coordinate physics proceeds differently by not introducing space-time coordinates in the first place. Differentials taken…