Related papers: The system of uniformly accelerating observers
We propose a simple nonlinear observer for estimating the attitude and velocity of a rigid body from the measurements of specific acceleration, angular velocity, magnetic field (in body axes), and linear velocity (in body axes). It is…
After a review of the existing theory of non-inertial frames and mathematical observers in Minkowski space-time we give the explicit expression of a family of such frames obtained from the inertial ones by means of point-dependent Lorentz…
The longitudinal Doppler shift is a measure of hyperbolic distance. Transformations of uniform motion are determined by the Doppler shift, while its square root transforms to a uniformly accelerated frame. A time-velocity space metric is…
The design of a globally convergent position observer for feature points from visual information is a challenging problem, especially for the case with only inertial measurements and without assumptions of uniform observability, which…
We investigate the possible structures of numbers (as physical quantities) over which accelerated observers can be modeled in special relativity. We present a general axiomatic theory of accelerated observers which has a model over every…
This paper considers the problem of simultaneous estimation of the attitude, position and linear velocity for vehicles navigating in a three-dimensional space. We propose two types of hybrid nonlinear observers using continuous angular…
A hybrid observer is described for estimating the state of a system of the form dot x=Ax, y_i=C_ix, i=1,...,m. The system's state x is simultaneously estimated by m agents assuming agent i senses y_i and receives appropriately defined data…
It is shown without making use of Lorentz transformation that there exists a phenomenon of relativistic zero-frequency shift in Doppler effect for a plane wave in free space, observed in two inertial frames of relative motion, and the zero…
A coordinate system is constructed for a general accelerating observer in 1+1 dimensions, and is used to determine the particle density of the massless Dirac vacuum for that observer. Equations are obtained for the spatial distribution and…
The method to design exponentially stable adaptive observers is proposed for linear time-invariant systems parameterized by unknown physical parameters. Unlike existing adaptive solutions, the system state-space matrices A, B are not…
We consider the problem of the period measurement in the case of the following scenarios: stationary source of successive light signals and accelerating receiver, stationary receiver and accelerating source of successive light signals and…
A challenge in teaching about special relativity is that a number of the theory's effects are at odds with the intuition of classical physics, as well as student's everyday experience. The relativity of simultaneity, time dilation and…
Fundamental to the analysis of nonlinear relativistic motion is the precise characterization of the induced dynamic Doppler effects. In this work, we analyze the electromagnetic signals observed by non-inertial receivers using two…
The particle detector model consisting of a harmonic oscillator coupled to a scalar field in $1+1$ dimensions is investigated in the inertial case. The same approach is then used in the accelerating case. The absence of radiation from a…
This paper addresses the problem of estimating the position of an object moving in $R^n$ from direction and velocity measurements. After addressing observability issues associated with this problem, a nonlinear observer is designed so as to…
A monochromatic linear source of light is rotated with certain angular frequency and when such light is analysed after reflection then a change of frequency or wavelength may be observed depending on the location of the observer. This…
In Minkowski space, an accelerated reference frame may be defined as one that is related to an inertial frame by a sequence of instantaneous Lorentz transformations. Such an accelerated observer sees a causal horizon, and the quantum vacuum…
An observer, in rectilinear motion under constant proper acceleration, passes near a source of monochromatic radiation at rest. In the context of special relativity, we describe the observed Doppler effect. We describe also the interesting…
An uniformly accelerated observer can build his proper system of coordinates in a delimited sector of the flat Minkowski spacetime. The properties of the position and time coordinate lines for such an observer are studied and compared with…
We give a rigorous derivation of the general-relativistic formula for the two-way Doppler tracking of a spacecraft in Friedmann-Lemaitre-Robertson-Walker and in McVittie spacetimes. The leading order corrections of the so-determined…