Related papers: The system of uniformly accelerating observers
We show that standard Relativistic Dynamics Equation F=dp/d\tau is only partially covariant. To achieve full Lorentz covariance, we replace the four-force F by a rank 2 antisymmetric tensor acting on the four-velocity. By taking this tensor…
This paper addresses the problem of estimating the relative pose (position and orientation) and velocity of a vehicle with respect to a moving target, where both are equipped with Inertial Measurement Units (IMUs), assuming the availability…
We consider a clock 'paradox' framework where an observer leaves an inertial frame, is accelerated and after an arbitrary trip comes back. We discuss a simple equation that gives, in the 1+1 dimensional case, an explicit relation between…
This paper introduces an advanced Lyapunov stability analysis for an attitude observer that has been developed on the special orthogonal group. In particular, when the attitude observer is constructed based on multiple direction…
This paper explores the observability and estimation capability of dynamical systems using predominantly relative measurements of the system's state-space variables, with minimal to no reliance on absolute measurements of these variables.…
We consider a radiation from a uniformly accelerating harmonic oscillator whose minimal coupling to the scalar field changes suddenly. The exact time evolutions of the quantum operators are given in terms of a classical solution of a forced…
We propose a globally exponentially convergent observer for the dynamical system evolving on matrix Lie groups with bounded velocity with unknown bound. We design the observer in the ambient Euclidean space and show exponential convergence…
The nonlocal theory of accelerated systems is extended to linear gravitational waves as measured by accelerated observers in Minkowski spacetime. The implications of this approach are discussed. In particular, the nonlocal modifications of…
In this work we discuss the process of measurements by a detector in an uniformly accelerated rectilinear motion, interacting linearly with a massive scalar field. The detector model for field quanta is a point-like system with a ground…
Static observers in curved spacetimes may interpret their proper acceleration as the opposite of a local gravitational field (in the Newtonian sense). Based on this interpretation and motivated by the equivalence principle, we are led to…
A cellular automata approach using a Directed Cyclic Graph is used to model interrelationships of fluctuating time, state and space. This model predicts phenomena including a constant and maximum speed at which any moving entity can travel,…
Formal definition of the reference frame is given. This definition is valid for nonrelativistic and relativistic cases. Proposed definition allows using wide classes of reference frames without restriction to inertial, uniformly accelerated…
A simple gedankenexperiment is proposed showing observability of radiation by an observer comoving with an accelerated charge.
An inversion transformation applied to an inertial observer is used to generate a nonstatic conformally flat geometry in spherical coordinates. A static observer in the new geometry is uniformly accelerating with respect to the inertial one…
The Unruh effect states that a uniformly linearly accelerated observer with proper acceleration $a$ experiences the Minkowski vacuum as a thermal state at temperature $T_U=a/(2\pi)$. An observer in uniform circular motion experiences a…
Motivated by drone autonomous navigation applications we address a novel problem of velocity-aided attitude estimation by combining two linear velocity components measured in a body-fixed frame and a linear velocity component measured in an…
The empirical formula proposed by J. D. Anderson et al. [1] to reproduce the data on the Earth flyby anomalies is derived from special relativity (SR). The transverse Doppler shift together with the addition of velocities account for the…
In this paper, existence conditions and a design procedure of reduced-order switched positive observers for continuous- and discrete-time switched positive linear systems with uncertainty are established. In the analyzed class, arbitrary…
This paper concerns the distributed observer for the descriptor linear system. Unlike centralized descriptor system observers, in the case of distributed observers, each agent either finds it difficult to independently eliminate impulses,…
We study the problem of parameters estimation in Indirect Observability contexts, where $X_t \in R^r$ is an unobservable stationary process parametrized by a vector of unknown parameters and all observable data are generated by an…