Related papers: Simplified Gyroscopic Treatment
We strengthen the case that the new logical perspective afforded by topos theory is suitable to the task of describing the physical world around us. In exploring some of the aspects of construction of a simple quantum-mechanical system in a…
This paper presents a brief but comprehensive introduction to certain mathematical techniques in General Relativity. Familiar mathematical procedures are investigated taking into account the complications of introducing a non trivial…
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.
The science of complexity is far from being fully understood and even its foundations are not well established. On the other hand, during the last decade, the random motion of particles or waves - the so-called diffusion - has been known…
This text is a short but comprehensive introduction to the basics of supergeometry and includes some of the recent advances in colored supergeometry. We do not aim for a standard text that states results and proves them more or less…
Systematic observations of student gestures can not only fill in gaps in students' verbal expressions, but can also offer valuable information about student ideas, including their source, their novelty to the speaker, and their construction…
In order to describe natural phenomena, science develops sophisticated models that use mathematical and formal languages which seem, and often are, very far from common experience. When a phenomenon is not accessible to our senses, its…
A new proof of the geodesic character of all motions of bodies that interact only gravitationally - and a detailed illustration of the real meaning of the linearized approximation of general relativity.
Explanation methods aim to make neural networks more trustworthy and interpretable. In this paper, we demonstrate a property of explanation methods which is disconcerting for both of these purposes. Namely, we show that explanations can be…
The physics of gravitational wave and its detection in the recent experiment by the LIGO collaboration is discussed in simple terms for a general audience. The main article is devoid of any mathematics, but an appendix is included for…
This is an expository article/encyclopedia entry explaining the history, techniques, and central results in the field of smooth ergodic theory.
Approximate equations are derived for the motion of a gyroscope on the earth's gravitational field using the Einstein, Infeld, Hoffmann surface integral method. This method does not require a knowledge of the energy-momentum-stress tensor…
The motion of a pendulum is described as Simple Harmonic Motion (SHM) in case the initial displacement given is small. If we relax this condition then we observe the deviation from the SHM. The equation of motion is non-linear and thus…
This is a short introduction of the exterior form formalism focus on its applications in physics and then mostly aimed to physics students. As a rule of a game played here we never use a coordinate frame neither in the definitions nor in…
We present a general approach for the formulation of equations of motion for compact objects in general relativistic theories. The particle is assumed to be moving in a geometric background which in turn is asymptotically flat. Our approach…
Quasistatics is introduced so that it fits smoothly into the standard textbook presentation of electrodynamics. The usual path from statics to general electrodynamics is rather short and surprisingly simple. A closer look reveals however…
We derive a gyrokinetic formalism which is very generally valid: the ordering allows both large inhomogeneities in plasma flow and magnetic field at long wavelength, like typical drift-kinetic theories, as well as fluctuations at the…
What does it mean to "make sense" of physics? It's not a simple question. Most people have an intuitive feeling for when things do (or do not) make sense to them. But, putting this feeling into words--especially actionable words--is another…
In this paper, we discuss the question whether a physical "simplification" of a model makes it always easier to study, at least from a mathematical and numerical point of view. To this end, we give different examples showing that these…
A Generalized Kinetic Theory was proposed in order to have the possibility to treat particles which obey a very general statistics. By adopting the same approach, we generalize here the Kinetic Theory of electrons and phonons. Equilibrium…