相关论文: From Kepler's laws to Newton's law: a didactical p…

The validity of Kepler Laws for the {\it spherical Kepler problem} -- namely, the problem of the motion of a particle on the unit sphere {in $\mathbb R^3$} undergoing an attraction by another particle in the sphere, tangent to the geodesic…

Considering the hyperbolic nature of the universe, the Hubble's law and the inverse square laws such as, the Coulomb's law and Newton's gravitational law, should be modified in accordance with the special theory of relativity. Consequently…

This article provides a simple geometric interpretation of the quadratic formula. The geometry helps to demystify the formula's complex appearance and casts it into a much simpler existence, thus potentially benefits early algebra students.

This article is the first article of a serie of articles on the generalization of Kato's Euler system. The main subject of this article is to construct a family of Kato's Euler systems and a family of Kato's explicit reciprocity laws over…

Corrections to Newton's inverse law have been so far considered, but not clear in warped higher dimensional worlds, because of complexity of the Einstein equation. Here we give a model of a warped 6D world with an extra 2D sphere. We take a…

Newton's second law has limited scope of application when transient phenomena are present. We consider a modification of Newton's second law in order to take into account a sudden change (surge) of angular momentum or linear momentum. We…

Using precession of orbits due to non-Newtonian interaction between two celestial bodies and modern tracking data of satellites, planets and a pulsar we obtain new more precise limits on possible Yukawa-type deviations from the Newton law…

Inspired by a didactic experience in an academic environment, and following the idea given by M. Villa in \cite{Villa}, we illustrate two different proofs of an important result in Euclidean geometry studied in the first two years of…

In teaching the physical sciences, a significant challenge lies in the student's tendency to consider the scientific world and the "real" world as separate. For example, Newton's 1st Law of Motion states that an object in motion remains in…

We consider a linearized, effective quantum theory of gravitation in which gravity weakens at energies higher than ~10^-3 eV in order to accommodate the apparent smallness of the cosmological constant. Such a theory predicts departures from…

We study arithmetic distribution relations and the inverse function theorem in algebraic and arithmetic geometry, with an emphasis on versions that can be applied uniformly across families of varieties and maps. In particular, we prove two…

As an expansion of complex numbers, the quaternions show close relations to numerous physically fundamental concepts. In spite of that, the didactic potential provided by quaternion interrelationships in formulating physical laws are hardly…

That preferred-frame theory accounts for special relativity and reduces to it if the gravitation field cancels. Starting from an interpretation of gravity as a pressure force, it is based on just one scalar field. This scalar gives the…

Kepler's first law states that the orbit of a point mass with negative energy in a classical gravitational potential is an ellipse with one of its foci at the gravitational center. In numerical simulations of this system one often observes…

One of the goals that physicists have been pursuing is to get the same explanation from different angles for the same phenomenon, so as to realize the unity of basic physical laws. Geometry, classical mechanics and classical thermodynamics…

Riemann's principle "force equals geometry" provided the basis for Einstein's General Relativity - the geometric theory of gravitation. In this paper, we follow this principle to derive the dynamics for any static, conservative force. The…

A generalization of classical dimensional analysis, presented in a separate article, makes it possible to derive Kepler's third law for the period of a two-body system, up to a multiplicative constant, without solving the equations of…

The problem of derivation of the equations of motion from the field equations is considered. Einstein's field equations have a specific analytical form: They are linear in the second order derivatives and quadratic in the first order…

Newton's laws of motion pose an apparent problem, sometimes referred to as "the independence problem": the first law seems to be a simple consequence of the second law, raising the question of why it was included as a separate law. Numerous…

We outline two subjects of relativistic mechanics: (i) the set of allowable world lines, and (ii) the origin of the relativistic law of dynamics governing point particles. We show that: (i) allowable world lines in the classical theory of…