相关论文: Using ordinary multiplication to do relativistic v…

A simple formal procedure makes the main properties of the lagrangian binomial extendable to functions depending to any kind of order of the time--derivatives of the lagrangian coordinates. Such a broadly formulated binomial can provide the…

This contribution shows that the main topics of Relativity can be discussed at an elementary level and in a considerable extent - including the formal results of "Time Dilation" and "Lorentz Contraction" - by a minor modification of the…

A method of determining two factors of an odd integer without need of multiplication or division operation in iterative portion of computation is presented. It is feasible for an implementing algorithm to use only integer addition and…

For certain problems involving vector fields, it is possible to find an associated imaginary field that, in conjunction with the first, forms a complex field for which the equation can be solved. This result is generalized to arbitrary…

We consider secular perturbations of nearly Keplerian two-body motion under a perturbing potential that can be approximated to sufficient accuracy by expanding it to second order in the coordinates. After averaging over time to obtain the…

We consider relativistic charged particle dynamics and relativistic magnetohydrodynamics using symplectic structures and actions given in terms of co-adjoint orbits of the Poincar\'e group. The particle case is meant to clarify some points…

Newton's law of motion relative to an inertial frame ("the laboratory") for a particle subject to a force acting at a certain time may be interpreted in either of two ways: (1) The force acting on the particle during an infinitesimal time…

We demonstrate that in the case of Schwarzschild spacetime the Doppler shift is partially factorized into terms representing relativistic, kinematical and the gravitational contributions. The condition for the complete factorization is…

We present an in depth analysis and a new derivation of the Doppler factor in the Lienard-Wiechert potentials, based on geometrical considerations in Minkowski space. We argue that, contrary to a common assumption, the methods used for…

We introduce an analytic method which stably reconstructs both components of a (sufficiently) smooth, real valued, vector field compactly supported in the plane from knowledge of its Doppler transform and its first moment Doppler transform.…

We give a brief critical examination of the special theory of relativity and a similar Newtonian framework to the first order of the $v/c$ ratio, focusing on the phenomena of aberration, Fresnel dragging, and the Doppler effect. We will…

Proceeding like Newton with a discrete time approach of motion and a geometrical representation of velocity and acceleration, we obtain Kepler's laws without solving differential equations. The difficult part of Newton's work, when it calls…

The kinematics of a particle with the upper bound on the particle's speed (a modification of classical kinematics where such a restriction is absent) has been developed in [arXiv:1204.5740]. It was based solely on classical mechanics…

Motivated by children inventing creatively laws on how to add or multiply fractions, we introduce four fraction operations and discover some of their properties.

Quaternions have an (over a century-old) extensive and quite complicated interaction with special relativity. Since quaternions are intrinsically 4-dimensional, and do such a good job of handling 3-dimensional rotations, the hope has always…

A gravitational theory with derivative matter coupling is proposed which adopt de Sitter expansion at late times with ordinary baryonic matter. Matter components are conserved separately in the cosmological background and the Newtonian…

Different relativistic quantum mechanics approaches have recently been used to calculate properties of various systems, form factors in particular. It is known that predictions, which most often rely on a single-particle current…

Relativity, time reversal invariance in mechanics and principle of causality can be in the bases of a type of vibration of the extensive objects. It is because, the detailed analysis of the relativistic movement of an extensive body entail…

This note generalizes factorization for formulas with multiplicities and conjectures that the connection method along with this feature is computationally as powerful as resolution, also seen from a complexity point of view.

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…