相关论文: The Frenet Frame as a Generalization of the Park T…
The paper discusses the relationships between electrical quantities, such as voltages, currents, and frequency, and geometrical ones, namely curvature and torsion. The proposed approach is based on the Frenet frame utilized in differential…
A one-dimensional space curve in $\mathbb{R}^{3}$ is a useful nonlinear medium for modeling vortex filaments and biological soft-matter capable of supporting a variety of wave motions. The Hasimoto transformation defines a mapping between…
We develop a transfer matrix formalism to visualize the framing of discrete piecewise linear curves in three dimensional space. Our approach is based on the concept of an intrinsically discrete curve, which enables us to more effectively…
This paper describes the foundations of a differential geometry of a quaternionic curves. The Frenet-Serret equations and the evolutes and evolvents of a particular quaternionic curve are accordingly determined. This new formulation takes…
The analysis of curves has been routinely dealt with using tools from functional data analysis. However its extension to multi-dimensional curves poses a new challenge due to its inherent geometric features that are difficult to capture…
Geometric frameworks for analyzing curves are common in applications as they focus on invariant features and provide visually satisfying solutions to standard problems such as computing invariant distances, averaging curves, or registering…
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…
A general theory of frames of reference proposed in a preceding publication is considered here in the framework of the post-Newtonian approximation, assuming that the frame of reference is centered on a time-like geodesic. The problem of…
In standard quantum mechanics, reference frames are treated as abstract entities. We can think of them as idealized, infinite-mass subsystems which decouple from the rest of the system. In nature, however, all reference frames are realized…
The increasing demand for Fourier transforms on geometric algebras has resulted in a large variety. Here we introduce one single straight forward definition of a general geometric Fourier transform covering most versions in the literature.…
The paper is devoted to differential geometric invariants determining a Frenet curve in up to a direct similarity These invariants can be presented by the Euclidean curvatures in terms of an arc lengths of the spherical indicatrices. Then,…
The Frenet-Serret curve analysis is extended from nonnull to null trajectories in a generic spacetime using the Newman-Penrose formalism, recovering old results which are not well known and clarifying the associated Fermi-Walker transport…
This paper proposes a general framework to interpret the concept of Instantaneous Frequency (IF) in three-phase systems. The paper first recalls the conventional frequency-domain analysis based on the Fourier transform as well as the…
Fourier representation (FR) is an indispensable mathematical formulation for modeling and analysis of physical phenomenon, engineering systems and signals in numerous applications. In this study, we present the generalized Fourier…
The main drawback of the Frenet frame is that it is undefined at those points where the curvature is zero. Further- more, in the case of planar curves, the Frenet frame does not agree with the standard framing of curves in the plane. The…
A novel geometrically exact model of the spatially curved Bernoulli-Euler beam is developed. The formulation utilizes the Frenet-Serret frame as the reference for updating the orientation of a cross section. The weak form is consistently…
In this paper, we investigate some characterizations of involute -- evolute curves in dual space. Then the relationships between dual frenet frame and darboux vectors of these curves are found.
Quantum reference frame transformations have been proposed to provide a means by which to translate descriptions of quantum systems relative to each other. At present, there are several differing frameworks for describing quantum reference…
We define a Frame of reference as a two ingredients concept: A meta-rigid motion, which is a generalization of a Born motion, and a chorodesic synchronization, which is an adapted foliation. At the end of the line we uncover a low-level…
A transition of focus from state space to frames of reference and their transformations is argued as being the appropriate setup for ensuring the covariance of physical laws. Such an approach can not only simplify and clarify aspects of…