Modeling Dynamic Systems: How does the Moon move?

Modeling Dynamic Systems: How does the Moon move? The bright memory of my teacher - the first dean of the Physics and Mathematics Faculty of the Novocherkassk Polytechnic Institute, the head of the department "Theoretical Mechanics" Alexander N. Cabelkova
 
 

Introduction


 
 
August, summer is coming to an end. The people furiously jerked to the seas, but it is not surprising - the season itself. And on the habra, meanwhile, In a violent color, pseudoscience disintegrates and smells. . If we talk about the topic of this issue of "Modeling ", then we will combine business with pleasure - we will continue the promised cycle and quite ...[/h]
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An infinite algorithmic melody based on primes

An infinite algorithmic melody based on primes

 
Hello, Habr! In the last article "An infinite pattern based on prime numbers" I talked about an algorithm that allows you to generate endless beautiful patterns that look like aliens, or something technological, like a microcircuit device. However, the algorithm for generating 2D patterns can also be used to create melodies. More under the cut.
 
here .
 
 
The program for generating music can be viewed here . It's called simple_sound. Ready exe can be found in the archive. At the output, the program creates a WAV file ...
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Probable method of mining Bitcoin

Probable method of mining Bitcoin  
 
I think a little delirium on Tuesday will not hurt much the working week.
 
I have a hobby, at leisure I try to figure out how to crack the bitcoin mining algorithm, avoid a dull nonsense search and find the solution to the problem of selecting a hash with a minimum energy consumption. Immediately I say the result, of course, I have not yet achieved, but nevertheless, why not put into writing the ideas that are born in the head? Where do you need to put them
 
 
Despite the delusionality of the ideas below, I think this article can be useful to someone who studies
 
 
 
C ++ language and its templates
 
a b...
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The construction of the orbits of celestial bodies using Python

The construction of the orbits of celestial bodies using Python  
 

Reference system for determining the orbit


 
To find the trajectories of relative motions in classical mechanics, we use the assumption of absolute time in all reference frames (both inertial and non-inertial).
 
 
Using this assumption, let us consider the motion of one and the same point in two different reference frames K and K ', of which the second moves relative to the first with an arbitrary speed  
 
We shall describe the motion of a point in the system K 'by the radius vector :
 
 
 
 
and the relative velocity is  
 
 
mathcad .
     Reference system for determining the orbit  To find the trajectories of relative motions in classical mechanics, we use the assumption of absolute time in all reference frames (both inertial and non-inertial).  Using this assumption, let us consider the motion of one and the same point in two different reference frames K and K ', of which the second moves relative to the first with an arbitrary speed   We shall describe the motion of a point in the system K 'by the radius vector :     and the relative velocity is      mathcad . ...[/h]
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Some problems of school mathematics

Based on articles "About one task that is no longer offered at the interview."
 
 
First, let's look at a task that you can still offer at an interview.
 
 
38. Calculate the amount ("Tasks for children from 5 to 15 years")
 
 
Some problems of school mathematics
 
(with an error of not more than 1% of the answer)
 
 
The algorithm for calculating the partial sums of this series in the language Scheme (Lisp) in the drRacket environment (drRacket allows to perform calculations in ordinary fractions):
 
#lang racket
(define series_sum
(lambda (n)
(if (= n 0) 0
(+ (/1 (* n (+ n 1))) (series_sum (- n 1)))
)) )
(series_sum 10)
(series_sum ...
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How technical indicators are arranged in the stock markets

Anyone who has ever been interested in stock or crypto-currencies has seen these additional lines. And you probably heard the opinions of the experienced traders that they do not work and how they do not use anything. But they help a lot and my trading terminal, which I lazily look at once a day, looks something like the picture below.
 
 
How are they arranged? And to whom it can be useful? You should definitely read this if:
 
 
 
You use them in your trade
 
You plan to write a trading robot
 
You want to implement the trading strategy yourself
 
 
How technical indicators are arranged in the stock markets
 
...
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On the formation of sequences in the Collatz conjecture (3n + 1)

On the formation of sequences in the Collatz conjecture (3n + 1)I am attracted by such problems as the Collatz problem. They are simple in the formulation and perfectly train the head, especially algorithmic thinking, which is very useful for the programmer.
 
 
The problem is formulated quite simply:
 
We take any natural number n. If it is even, then divide it by ? and if it is odd, then multiply by 3 and add 1 (we get 3n + 1). Above the number obtained, we perform the same actions, and so on.
 
The Collatz conjecture is that whatever initial number n we take, sooner or later we get unity.
 
 
Algorithmically it looks like this:
 
 
...
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Numerical methods for solving equations of elliptic type

Numerical methods for solving equations of elliptic type

Introduction


 
The most common equation of the elliptic type is the Poisson equation.
 
Many problems of mathematical physics are reduced to the solution of this equation, for example, problems of the stationary temperature distribution in a solid, diffusion problems, problems of the distribution of an electrostatic field in a nonconducting medium in the presence of electric charges, and many others.
 
 
To solve elliptic equations in the case of several measurements, numerical methods are used that allow one to transform differential equations or their systems into systems of algebraic equations...[/h]
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Calculation of wave processes in a hydraulic line by the method of characteristics

Calculation of wave processes in a hydraulic line by the method of characteristics  
 
Hello, Habr! In this article, I'll talk about creating a mathematical model of a long pipeline for the SimulationX CAE program in Modelica. We will talk about the calculation of wave processes (pressure pulsations, hydraulic shock, etc.) in the hydraulic line by the method of characteristics. Despite the fact that this method is quite old, there is very little information about its application for solving applied problems in runet.
 
 
Under the cut I will try to explain why we need to take into account the wave processes in the pipelines, highlight the problems that I encountered in programming, and ...
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How much does a programmer need to know math?

Recently I went on the Net and met all kinds of opinions about whether a mathematician is necessary at all, and if so, how much. I'll try to generalize and sum up.
 
 
To begin with, it should be noted that mathematics in our lives is present almost everywhere. Physics without mathematics is unthinkable - here, I think, everything is clear, and there is no need to explain. Chemistry, too. In biology, the influence of mathematics is noticeably less, but even there it is present (take, for example, plant structures, many of them quasifractals).
Music can be represented in mathematical form. Unthinkable ...
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