kaname.hirano

Analysis

Numerical Solution of Ordinary Differential Equations

This article will provide an overview of the Euler method and the Runge-Kutta method as numerical methods for solving ordinary differential equations with initial conditions. For equations that cannot be solved analytically, we will use numerical methods to explain them.
2024.09.18
Analysis
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.
2024.09.13
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.
2024.09.08
Probability
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.
2024.09.03
Physics
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.
2024.08.30
Probability
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.
2024.08.25
Physics
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.
2024.08.18
Physics
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.
2024.08.11
AnalysisPhysics
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.
2024.08.06
Physics
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.
2024.08.02
Analysis
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