## March 6th, 2020

### Ньютон и мой любимый алгоритм Верле

Newton's discrete dynamics: https://arxiv.org/abs/2003.02702

In 1687 Isaac Newton published PHILOSOPHIÆ\ NATURALIS PRINCIPIA MATHEMATICA, where the classical analytic dynamics was formulated. But Newton also formulated a discrete dynamics, which is the central difference algorithm, known as the Verlet algorithm. In fact Newton used the central difference to derive his second law. The central difference algorithm is used in computer simulations,where almost all Molecular Dynamics simulations are performed with the Verlet algorithm or other reformulations of the central difference algorithm. Here we show, that the discrete dynamics obtained by Newtons algorithm for Kepler's equation has the same solutions as the analytic dynamics. The discrete positions of a celestial body are located on an ellipse, which is the exact solution for a shadow Hamiltonian nearby the Hamiltonian for the analytic solution.

### Как наматывать ВТСП-магниты

Не вчитывался, но, похоже, техническое использование высокотемпературных сверхпроводников вполне себе прогрессирует:

Non-Planar Coil Winding Angle Optimization for Compatibility with Non-Insulated High-Temperature Superconducting Magnets: https://arxiv.org/abs/2003.02154

### Что-то популярное о теории относительности

Вроде и Беркли, а все равно у них масса зависит от скорости...

Simple Relativity Approach to Special Relativity: https://arxiv.org/abs/2002.12118

The development of both special and general relativity is accomplished in a series of 6 papers using a simple approach. The purpose is to explain the how and why of relativity to a broad public, and to be useful for students of physics by providing alternate ways to develop and view relativistic phenomena. In this first paper, the rules for special relativity are developed to explain velocity-related time dilation and length contraction, and the interchangeable nature of mass and energy. In subsequent papers, conservation of energy is applied to show how gravity affects time speed, fall velocities, and length measurements, the effect known as the Shapiro Time Delay, the precession of satellites and planets, gravitational lensing, the appearance of Lorentz contraction and a simple resolution of the Ehrenfest paradox.