Related papers: A Historical Method Approach to Teaching Kepler's …
This contribution analyses the classical laws of motion by means of an approach relating time and entropy. We argue that adopting the notion of change of states as opposed to the usual derivation of Newton's laws in terms of fields a…
Lambert's theorem (1761) on the elapsed time along a Keplerian arc drew the attention of several prestigious mathematicians. In particular, they tried to give simple and transparent proofs of it (see our timeline \S 9). We give two new…
We review different studies of the Periodic Law and the set of chemical elements from a mathematical point of view. This discussion covers the first attempts made in the 19th century up to the present day. Mathematics employed to study the…
The arrow of time dilemma: the laws of physics are invariant for time inversion, whereas the familiar phenomena we see everyday are not (i.e. entropy increases). I show that, within a quantum mechanical framework, all phenomena which leave…
This work gives a brief summary of major formulations of the third law of thermodynamics and their implications, including the impossibility of perpetual motion of the third kind. The last sections of this work review more advanced…
We explain the solution of the following two problems: obtaining of Kepler's laws from Newton's laws (so called two bodies problem) and obtaining the fourth Newton's law (the formula for gravitation) as a corollary of Kepler's laws. This…
A goal of physics is to understand the greatest possible breadth of natural phenomena in terms of the most economical set of basic concepts. However, as the understanding of physics has developed historically, its pedagogy and language have…
In the paradigmatic example of quantum measurements, whenever one measures a system which starts in a superposition of two states of a conserved quantity, it jumps to one of the two states, implying different final values for the quantity…
We propose a discussion of angular momentum and its Euler equation, with the aim of giving a short outline of their history. This outline can be useful for teaching purposes too, to amend some problems that students can have in learning…
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…
Vectorial analysis relating to derivation of deflection of light is presented. Curvilinear acceleration is distinguished from the Newtonian polar conic acceleration. The difference between the two is due to the curvature term. Lorentz…
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…
A mathematical model is given for the occurrence of preferred orbits and orbital velocities in a Keplerian system. The result can be extended into energies and other properties of physical systems. The values given by the model fit closely…
The space-time length R between a moving source and the observation point is calculated in order to substitute with it the spatial distance D, normally used in the Newton's law of gravitation, as well as in any inverse-square-law.…
We explore the relationship between mechanical systems describing the motion of a particle with the mechanical systems describing a continuous medium. More specifically, we will study how the so-called intermediate integrals or fields of…
The aim of this work is to continue the analysis, started in arXiv:2105.02108, of the dynamics of a point-mass particle $P$ moving in a galaxy with an harmonic biaxial core, in whose center sits a Keplerian attractive center (e.g. a Black…
The discovery of quantum mechanics at the beginning of the last century led to a revolution of the physical world view. Modern experiments, made possible by new techniques on the border of the classical and the quantum regimes offer new…
Incompressible two-dimensional flows such as the advection (Liouville) equation and the Euler equations have a large family of conservation laws related to conservation of area. We present two Eulerian numerical methods which preserve a…
This thesis is concerned with the representation theory of the Heisenberg group and its applications to both classical and quantum mechanics. We continue the development of $p$-mechanics which is a consistent physical theory capable of…
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…