Related papers: On the construction of Fermi-Walker transported fr…
The local bounded commuting projection operators of nonstandard finite element de Rham complexes in two and three dimensions are constructed systematically. The assumptions of the main result are mild and can be verified. For three…
We generalize Fermi coordinates, which correspond to an adapted set of coordinates describing the vicinity of an observer's worldline, to the worldsheet of an arbitrary spatial curve in a static spacetime. The spatial coordinate axes are…
Relative attitude formation control systems are developed for multiple spacecraft, based on the line-of-sight measurements between spacecraft in formation. The proposed control systems are unique in the sense that they do not require…
In this work, we use a minimal model to introduce a framework for controlling self-assembly under the influence of time-dependent driving forces. We develop a mean-field thermodynamic framework that predicts the conditions required to…
In this methodological note we discuss several topics related to interpretation of some basic cosmological principles. We demonstrate that one of the key points is the usage of synchronous reference frames. The Friedmann-Robertson-Walker…
Fermi coordinates are constructed as exact functions of the Schwar\-zschild coordinates around the world line of a static observer in the equatorial plane of the Schwarzschild spacetime modulo a single impact parameter determined implicitly…
We study how to implement and transform frame perspectives for quantum processes in the process-matrix formalism. We argue that, for pure processes, the causal reference frames (CRF)and time-delocalized subsystems (TDS) formalisms should be…
Field-based reactive control provides a minimalist, decentralized route to guiding robots that lack onboard computation. Such schemes are well suited to resource-limited machines like microrobots, yet implementation artifacts, limited…
We present the gauge-invariant formalism of cosmological weak lensing, accounting for all the relativistic effects due to the scalar, vector, and tensor perturbations at the linear order. While the light propagation is fully described by…
We argue that correct account of the quantum properties of macroscopic objects which form reference frames (RF) demand the change of the standard space-time picture accepted in Quantum Mechanics. Galilean or Lorentz space-time…
A local criteria for the existence of an accelerated frame of reference is found. An accelerated frame of reference could exist in all regions where a non-null (non-isotropic) vector field does not degenerate in a null (isotropic) vector…
We take causality and uniqueness of events observation as our driving forces. They are built in in the way we define distinct observers, which then require a finite time to communicate between each other. This unavoidably leads to the…
In Tensor Field Theory (TFT), observables are defined through tensor field contractions that produce unitary invariants for complex-valued tensor fields. Traditionally, these observables are constructed using tensor fields of a fixed order…
The tetrad gauge invariant theory of the free Dirac field in two special moving charts of the de Sitter spacetime is investigated pointing out the operators that commute with the Dirac one. These are the generators of the symmetry…
According to the locality postulate of special relativity, the measurements of physical fields by accelerated observers at a given event in Minkowski spacetime are related to each other by the representations of the Lorentz group. Nonlocal…
We first develop systematic and comprehensive interval observer designs for linear time-invariant (LTI) systems, under standard assumptions of observability and interval bounds on the initial condition and uncertainties. Traditionally, such…
We revisit the definition of transverse frames and tetrad choices with regards to its application to numerically generated spacetimes, in particular those from the merger of binary black holes. We introduce the concept of local and…
The historical origins of Fermi-Walker transport and Fermi coordinates and the construction of Fermi-Walker transported frames in black hole spacetimes are reviewed. For geodesics this transport reduces to parallel transport and these…
The apparent times and positions of moving clocks as predicted by both `non-local' and `local' Lorentz Transformations are considered. Only local transformations respect translational invariance. Such transformations change temporal but not…
A new kind of uniformly accelerated reference frames with a line-element different from the M{\o}ller and Rindler ones is presented, in which every observer at $x, y, z=$consts. has the same constant acceleration. The laws of mechanics are…