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Worked Examples
Used Tools
Description

Mathematics

MonteCarlo.html
Mathematica 6

Title: Monte Carlo method.

The notebook contains the worked example of Monte Carlo method for computer simulation of N random points uniformly distributed on the sphere.

Cram.nb (47 KB),

Gram.pdf (201 KB)

 

Mathematica 6

Title: The problem of finding a linearly independent system of functions.

In the notebook, you can find three approaches to solving the problem.

Also, in the notebook there are calculations of Gram determinant and Wronskian.

Fredholm Integral Equation of the Second Kind.

.xmcd (27 KB zip)

Mathcad 14.0

This demonstrates indexing of functions in Mathcad.
1) Exact solution on condition that the kernel is degenerate
2) Net-method (transforming an integral into a finite sum)
3) Function approximation method
3.1) Collocation method
3.2) Least-square method
3.3) Galerkin method (projection operator technique)

Construction of a bounded region.

.xmcd (6 KB zip)

Mathcad 14.0

Demonstrates programming in Mathcad.

Linear system. (286 KB zip)

Delphi 7

Gaussian elimination method for linear system of algebraic equations.

Notes. 1) The program prints all the steps of the solution. 2) Data can be exported and imported in Excel format.

General bivariate regression
and integral equation.

.xmcd (9 KB zip)

Mathcad 14.0
General bivariate regression
and integral equation.

Mechanics and 3D Graphics

3D Scope (new)

(Microsoft Windows XP Professional 2002)

.exe (755 KB zip)

C++Builder 6,

OpenGL,

Mathematica 6.

The program simulates a rigid body motion.

The research paper is here (it is written in Russian).

Rigid Body project

.m (329 KB zip)

Matlab 7.5.0

The Rigid Body project demonstrates a rotation of a rigid body about a fixed point without regard for friction forces.

The project is made by using GUIDE of Matlab 7.5.0 (R2007b) and user-defined classes.

Ball Rolling without Slipping Inside a Vertical Cylinder.

.nb (91 KB zip)

Or visit Wolfram Demonstrations Projects site to look at the Wolfram demonstration project.

 

Mathematica 6

In the publication you can find:
1) The analytical solution of the equations of motion of a ball on the inside of a rough vertical cylinder. (The friction is disregarded.)
2) The visualization of the motion including a real-time visualization.
3) Some tricks for the better visualization ( the while loop together with the rotated arrow's indicator to get a real-time effect , the arrow3D object to get a 3D arrow , the Trace and the smartSphere objects to render a trajectory and a colored sphere quickly).

In the publication all of the formula derivations are generated by Mathematica 6. There is no one made in writing.

Asymmetric Top Free Rotation.

.nb (25 KB zip)

Or visit Wolfram Demonstrations Projects site to look at the Wolfram demonstration project.

Mathematica 6
The notebook demonstrates the inertial rotation of the asymmetric top about a fixed point. A common brick plays the part of the asymmetric top. The general properties of the motion are presented in the notebook.
The notebook may be used on the seminars on mechanics in the technical educational establishments.

3D Scope(old)

(Microsoft Windows XP Professional 2002)

.exe, .nb (2.7 MB zip)

 

C++Builder 6,

OpenGL,

Mathematica 6.

The program demonstrates the inertial rotation of the asymmetric top about a fixed point. A common brick plays the part of the asymmetric top. The general properties of the motion are presented in the program.
The program may be used on the seminars on mechanics in the technical educational establishments.

Regular Precession

.xmcd, .gif (373 KB zip)

Mathcad 14.0

Demonstrates animation in Mathcad.

Other examples

Universal Method of Rigid Body Motion Simulation.

.pdf (1.48 MB)

MO Word 2007, Math Type 6.0

It is a research paper (written in Russian).

ElementaryMathematicsTask.pdf (388 KB zip) ElementaryMathematicsTask.djvu (336 KB zip)

Microsoft Office Word 2007, Mathematica 6, Math Type 6.0

It is a problem book.

Brook.docm (287 KB zip)

Microsoft Office Word 2007, Visual Basic for Applications

It’s a keyboard trainer.

Look at the screenshot of the program and Help.html.

Presentation.pdf (1 MB) MO Word 2007 Application of computer technology in mechanics and mathematics.(It's written in Russian)
NOSE_THE_DWARF.pdf (398 KB) MO Word 2007

NOSE, THE DWARF

by Wilhelm Hauff

 


 

Updated on April 13, 2014