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

The hodograph of the Kepler-Coulomb problem, that is, the path traced by its velocity vector, is shown to be a circle and then it is used to investigate other properties of the motion. We obtain the configuration space orbits of the problem…

We consider the possibility of generalizing the Newtonian law of gravity and the transition to a general relativistic model for weak fields with the inclusion of a repulsive term identified as a cosmological constant. The analysis includes…

The k-calculus was advocated by Hermann Bondi as a means of explaining special relativity using only GCSE level mathematics and ideas. We review the central derivations, using proofs which are only a little more elegant than those in…

A specific form of the inertial law is presented by which we can have some deeper insight into the essence of mass and inertia. In this modified theory, there is no need to keep the concept of absolute space and Newton's third law as…

Newton's quadrilateral theorem can be phrased as follows. If H is a circle that is tangent to the four extended sides of a non-parallelogram quadrilateral Q, the center of H lies on the Newton line of Q. We prove that the theorem remains…

We will make the case that \textit{pedal coordinates} (instead of polar or Cartesian coordinates) are more natural settings in which to study force problems of classical mechanics in the plane. We will show that the trajectory of a test…

The Newton line and the associated theorems by Newton and Gauss for tetragons and quadrilaterals are closely linked to some other theorems of Euclidean geometry: a theorem by Bocher on the existence of a nine-point conic of a quadrangle, a…

We show that results of a simple dynamical gedanken experiment interpreted according to standard Newton's gravitational theory, may reveal that three-dimensional space is curved. The experiment may be used to reconstruct the curved geometry…

Deviations from Newton's Inverse-Squared Law at the micron length scale are smoking-gun signals for models containing Supersymmetric Large Extra Dimensions (SLEDs), which have been proposed as approaches for resolving the Cosmological…

Starting from first principles and general assumptions Newton's law of gravitation is shown to arise naturally and unavoidably in a theory in which space is emergent through a holographic scenario. Gravity is explained as an entropic force…

Aspects of quantum physics are no longer confined to the upper years of a physics degree. Concepts like superposition or entanglement that were once reserved for second- or third-year undergraduate courses now deserve attention earlier in a…

Using the quantum Hamilton-Jacobi equation within the framework of the equivalence postulate, we construct a Lagrangian of a quantum system in one dimension and derive a third order equation of motion representing a first integral of the…

The Bertrand's theorem can be formulated as the solution of an inverse problem for a classical unidimensional motion. We show that the solutions of these problems, if restricted to a given class, can be obtained by solving a numerical…

In this article we present an elementary introduction to the theory of minimal surfaces in Euclidean spaces $\mathbb R^n$ for $n\ge 3$ by using only elementary calculus of functions of several variables at the level of a typical second-year…

We investigated students' use of Newton's second law in mechanics and electromagnetism contexts by interviewing students in a two-semester calculus-based physics course. We observed that students' responses are consistent with three mental…

We present alternative postulates for Euclidean geometry whose merit is that they lead to a new class of invariants and associated geometries for real finite-dimensional unital associative algebras.

We apply Feynman's principle, ``The same equations have the same solutions'', to Kepler's problem and show that Newton's dynamics in a properly curved 3-D space is identical with that described by Einstein's theory in the 3-D optical…

This paper aims to provide teachers with a tool to teach the essential features of special relativity, considering the students' difficulties highlighted by numerous studies. Our proposal presents special relativity as the solution to the…

The spin geometry theorem of Penrose is extended from $SU(2)$ to $E(3)$ (Euclidean) invariant elementary quantum mechanical systems. Using the natural decomposition of the total angular momentum into its spin and orbital parts, the…

With consideration of quantization of space, we relate Newton's gravitation with the Second Law of thermodynamics. This leads to a correction to its original form, which takes into consideration the role of classical measurement. Our…