Related papers: Frames of Reference and Some of its Applications
Physics is a model of nature able to both describe and predict the results of measurements made with respect to reference systems. These reference systems, in turn, are themselves physical and thus subject to the laws of physics. The…
This paper is concerned with possibility of recovery of motion and structure parameters from multiframes under perspective projection when only points on a rigid body are traced. Free (unrestricted and uncontrolled) pattern of motion…
From higher dimensional theories, e.g. string theory, one expects the presence of non-minimally coupled scalar fields. We review the notion of conformal frames in cosmology and emphasize their physical equivalence, which holds at least at a…
In this paper a new concept related to the frame theory is introduced; the notion of pair frame. By investigating some properties of such frames, it is shown that pair frames are a generalization of ordinary frames. Some classes of of them…
Reference frames are used to parameterize measurements of physical effects, but since their practical realization uses material objects, they may affect observations performed in a combined quantum state of the measured system together with…
A parametric manifold can be viewed as the manifold of orbits of a (regular) foliation of a manifold by means of a family of curves. If the foliation is hypersurface orthogonal, the parametric manifold is equivalent to the 1-parameter…
This paper is devoted to the study of unparameterized simple curves in the plane. We propose diverse canonical parameterizations of a 2D-curve. For instance, the arc-length parameterization is canonical, but we consider other natural…
The main subject of the book is an up-to-date and in-depth survey of the theory of normal frames and coordinates in differential geometry. The book can be used as a reference manual, review of the existing results and introduction to some…
This article explores the differences between frame and coordinate transformations in relativistic theories. We highlight the key role of tetrad fields in connecting spacetime and frame indices. Using Maxwell's electrodynamics as an…
The pose of a rigid object is usually regarded as a rigid transformation, described by a translation and a rotation. However, equating the pose space with the space of rigid transformations is in general abusive, as it does not account for…
Transformation rules for coordinates, velocities and accelerations in accelerated reference frames are derived. A generalized approach of the special relativity is taken for a basis. A 7-dimensional space including projections of velocity…
A covariant reformulation of General Relativity is briefly considered from three points of view: geometrodynamics, Lagrange-Euler field theory, and gauge field theory. From a geometrodynamics perspective, a definition of the reference frame…
We postulate the applicability of the general form-invariance principle in special relativity. It is shown that this principle holds in classical mechanics. Some examples of transformations between the reference frames which satisfy this…
The recently introduced and characterized scalable frames can be considered as those frames which allow for perfect preconditioning in the sense that the frame vectors can be rescaled to yield a tight frame. In this paper we define…
This article suggests that thinking about the role of reference frames can provide new insight into Extended Wigner's Friend scenarios. This involves appealing to symmetries to make a principled distinction between properties of a system…
In a recent paper we discussed when it is possible to define reference frames nonrotating with respect to distant inertial reference objects (extension of the IAU reference systems to exact general relativity), and how to construct them. We…
A framework is a graph and a map from its vertices to R^d. A framework is called universally rigid if there is no other framework with the same graph and edge lengths in R^d' for any d'. A framework attachment is a framework constructed by…
The monopole singularity string, infinite direct line in the rest reference frame, is considered as a rigid physical line, and behavior of its geometrical form under the Lorentz transformations is studied. The method to test the form of any…
Finite frames can be viewed as mass points distributed in $N$-dimensional Euclidean space. As such they form a subclass of a larger and rich class of probability measures that we call probabilistic frames. We derive the basic properties of…
The frame set of a function $g\in L^2(\mathbb{R})$ is the subset of all parameters $(a, b)\in \mathbb{R}^2_+$ for which the time-frequency shifts of $g$ along $a\mathbb{Z}\times b\mathbb{Z}$ form a Gabor frame for $L^2(\mathbb{R}).$ In this…