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Lesson 1 - about mechanics

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Introduction

The whole our universe is filled with matter and various objects. Let's call them - bodies. All these bodies (and we people as well) are interacting with each other somehow. Generally, our world is very complex and we should accept the fact, that we know not much about it. However, things usually happen according to some patterns or rules. It is obviously very useful for us to know and understand such rules since they let us to predict behaviour of physical systemes and control them. Since as such is exactly concerned with studying and exploring such rules (or better - laws). In particular, "physics" explores the material interaction between bodies. This interaction can have different nature - mechanical, electromagnetical etc.

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Lesson 2 - Material Point and Rigid Body

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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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Lesson 3 - Force and Torque

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

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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.

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fig. 1.4.1 A system of forces and resulting force

The system of four forces applied to the airplane:

  • Thrust force Ft
  • Gravity force Fg
  • air Drag force Fd
  • air Lift force Fl
- replace them all with one equivalent force R

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Lesson 5 - Equilibrium and reactions

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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 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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