### last activities:

- 3/6/2019 DYsolve 2.5 for Windows, Mac OS X: Bug with greek and cyrillic encoding fixed.
- 2/25/2019 DYsolve 2.5, all versions updated. Functions for statistics introduced, new commands and tutorials added.
- 2/5/2019 DYsolve 2.5, Build 026 - Android: Non-linear equation solver implemented.
- 2/5/2019 DYsolve 2.5, Build 015 - Windows and Mac OS X: Non-linear equation solver implemented.
- 1/10/2019 DYsolve 2.5, Build 014 - for Windows and Mac OS X: Interface reworked, Expression preview, Multiline executor.
- 12/25/2018 DYsolve 2.4, Build 024 - Android: 3D Surface Grapher added! Some new functions to work with vectors.
- 12/10/2018 DYsolve 2.4, Build 012 - Mac OS X: Dysolve Math Solver is finally available on Mac OS X!
- 12/9/2018 DYsolve 2.4, Build 012 - Desktop: Surface Plots added, quick guide updated
- 10/18/2018 DYsolve 2.3, Build 023 - Android: Document editor implemented, new functions added.
- 9/25/2018 added new Chapter to the english version of theoretical mechanics course: "Adding forces, reducing a system of forces to a center".
- 9/25/2018 added new Chapter to the english version of theoretical mechanics course: "Force and Torque".
- 9/22/2018 added new Chapter to the english version of theoretical mechanics course: "Material Point and Rigid Body".
- 16.09.2018 Direct Scientific Calculator 1.1, build 003: Loading templates, Natural look, menu with system functions!
- 05.09.2018 Direct Scientific Calculator 1.0, build 002: Integrals and Function Limits added! Now can copy result from preview window!
- 31.08.2018 First version of Direct Scientific Calculator released! Now available in Google Play!
- 15.08.2018 DYsolve 2.2 for Android, Build 022: OpenGL implemented in 2D Plots. Polynomial support added. Video tutorials added.
- 15.08.2018 DYsolve 2.2, Build 011 - Desktop: OpenGL was implemented in 2D plots, polynomial support added.
- 24.07.2018 added first Chapter to the english version of theoretical mechanics course: "Introduction".
- 19.07.2018 added new Chapter to the theoretical mechanics course: "Solving problems of statics" (in russian).
- 08.07.2018 added new Chapter to the theoretical mechanics course: "Equilibrium and Reactions" (in russian).
- 23.06.2018 added new Chapter to the theoretical mechanics course: "Resulting Force" (in russian).
- 22.06.2018 DYsolve 2.1, Build 010: Definite Integrals and Limits of a functions now available in Desktop version.
- 20.06.2018 DYsolve 2.1 for Android, Build 020: Tools for solving definite Integrals and Limits of a functions added.
- 23.05.2018 DYsolve 2.1 for Android, Build 019: "Dynamic Data" option implemented in mobile version.
- 23.05.2018 DYsolve 2.1, Build 009: "Dynamic Data" option added. Now all data is updated after each user input.
- 08.04.2018 DYsolve 2.0 for Android, Build 014: Library with calculation examples added.
- 25.03.2018 DYsolve 2.0, Build 008: Web code updated in order to decrease server load.
- 14.03.2018 DYsolve 2.0 for Android, Build 013: has been released! Now mobile DYsolve is a web-application and can work together with desktop version.
- 05.02.2018 DYsolve 2.0, Build 007: Dysolve become a web application. You can save work on server, simple messenger is implemented (only desktop version).
- 27.01.2017 DYsolve 1.1, Build 005: dimensions added, not fully defined components can be created.
- 17.01.2017 DYsolve 1.1, Build 004: application's core is reworked.
- 15.11.2016 added russian version of DYsolve quickguide.
- 09.11.2016 published first chapters of Theoretical Mechanics basic course.
- 04.10.2016 mobile version of DYsolve now available on Google Play.
- 30.05.2016 DYsolve 1.0, Build 003: while loops, else blocks added.
- 09.05.2016 DYsolve 1.0, Build 002: arrays are available now.
- 05.05.2016 DYsolve 1.0, Build 001 for Windows added.
- 09.04.2016 DYsolve: Quick Guide added.
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### last publications:

## Lesson 6 - Solving problems of statics

### Internal and external loads

Regarding to the specific mechanical system, all loads can be divided into two groups: internal and external. As mentioned in lesson 3, solving of mechanical problem starts from mentally isolating mechanical system from the outer world, and replacing impacts from the surrounding bodies on our system with forces and torques. By "mechanical system" are meant a single body or a group of bodies, which are somehow interacting with the outer world.

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## Lesson 5 - Equilibrium and reactions

### Equilibrium

Equilibrium is a core concept of statics. Equilibrium of the body means that body is in the rest state relative to surrounding bodies. In other words, the body is static in some desired coordinate system. For instance, your house is in rest state (in equilibrium state) relative to the earth. The house isn't moving anywhere despite a set of forces is applied to him: gravity, background friction force, pressure of the fallen tree above the roof:

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## Lesson 4 - adding forces, reducing a system of forces to a center

Now you know that force is a vector quantity (as well as Torque). Several forces can be applied to mechanical system and it's usually a good step to simplify the system of forces, reducing them to one resulting force and one resulting torque. In order to do that we have to find a geometrical sum of force vectors.

The system of four forces applied to the airplane:

- Thrust force
*Ft* - Gravity force
*Fg* - air Drag force
*Fd* - air Lift force
*Fl*

*R*

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## Lesson 3 - Force and Torque

As you already know, the subject of mechanics is mechanical interaction between bodies. This interaction needs to be evaluated and measured somehow, since it has some intensity, area of application, direction. For this purpose the concept of "Force" is introduced. Force is a measure of power interaction between the bodies. This interaction occurs when bodies come in contact with each other.

Force is represented with a vector. This means, it has a magnitude (length), direction, line of impact and application point.

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## Lesson 2 - Material Point and Rigid Body

In order to simplify calculations in classical mechanics, real bodies are being substituted with their simplified models. Such models are Material Point and Rigid Body. All equations are based on these models. When you have a real object you need to simulate, you have to choose an appropriate model for it. There are no strict rules on how to do that, you just need to desire what model is most suitable for your case.

### Material Point

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