Physics Elliptical Motion in the Theory of Relativity
This article derives an equation of motion equivalent to the Schwarzschild solution from the theory of analytical mechanics in a conical coordinate system.
Physics 
Probability Probability Distribution on the Sphere
This article consider a probability distribution that is uniformly distributed on a sphere. In the case of a two-dimensional sphere, the probability distribution of each coordinate has a uniform distribution, and has some interesting properties.
Physics Two-body Problem
This article consider how the equations of motion for elliptical motion in classical mechanics, known as the two-body problem, can be formulated by rewriting the equations as if two masses were moving independently.
Probability How Machine Learning Works
Although it may seem a little late to be saying this, I feel like I've finally come to understand what makes machine learning different from other data analysis methods such as regression analysis and how it works, so I'll give a brief explanation here.
Physics Schrödinger Equation in the Free State (3 Dimensions)
In this article, we derive the solution to the three-dimensional Schrödinger equation when we consider a Gaussian wave packet model (white noise model) in the same way as in the one-dimensional case.
Physics Motion and Energy in the Theory of Relativity
Consider the hypothesis that the space-time of the theory of relativity is a conical coordinate system. We will summarize the discussion of what the equations of motion and conserved quantities are under this hypothesis, and show the problems.
Analysis Kepler Equation
The orbits of planets and other objects moving around stars are elliptical, but the angular velocity is not constant. We consider a method of finding a solution to an algebraic equation called the Kepler equation by using Bessel functions.
Physics Elliptical Motion in Classical Mechanics
This article consider elliptical motion in three-dimensional space. Typically, it would be the motion of a planet orbiting a large star such as the Sun.
Analysis Bessel Functions
Here is a brief summary of the properties of Bessel functions. They will be necessary when considering Kepler's equations (equations of elliptical motion) and the motion of electrons bound to atomic nuclei.
Physics Uniform Circular Motion in the Theory of Relativity
This article explain the theory of uniform circular motion in classical mechanics and extend it to the case of the theory of relativity.