Department of Theoretical Mechanics, Engineering and Robotic Systems (202)

227 m.b.
Teachers room 236 m.b.
Khai202.ho.ua

Assistant
Ternovskaya Svetlana Sergeevna

that deals with the mechanical motion of bodies, i.e. changing

of relative position of bodies in space in the course of time.

have uniform motion. Such bodies are said to be in

equilibrium.
Statics provides methods for determination of support reactions and relationships between internal force distribution and external loads for structures.

rigid body (абсолютно твердое тело)
A body is called rigid if

the distance between any two points of the body does not change during its interaction with other solids. Consequently, the angle between any two straight lines in the body remains constant
A rigid body system (система твердых тел)
A set of rigid bodies connected among themselves is called rigid body system

the bucket of a bulldozer. In engineering practice particle systems or

rigid body systems are more often called structures.

irrelevant to the description of its position the body may

by treated as a
particle.

A particle system (система материальных точек, материальная система)
A particle system is a set of particles whose motions are interconnected. So, a position, velocity and acceleration of particle in the system are connected with same parameters of other particles.
The sample of particle system is system of planets that rotates about the Sun.

quantities of mechanics.
A force is measure of mechanical interaction between

two bodies. So when we say “a force acts on the body” we know that there is another body acting as a source of the force.
As a result of this interaction bodies can be accelerated or deformed.

mechanics. We distinguish forces solely by the mode of their

interaction :
a force may be exerted at a distance as in the case of gravitational or magnetic attraction (long-range interaction);
a force may act through actual contact as the lift force acting on the airplane wing in incident flow
(close-range interaction)

magnitude, a direction and a point of application.

a material object (particle, rigid body, system of rigid bodies)

and treated as group is called system of forces.
Example. Forces that act on an airplane: tractive force, lift force, weight, drag force.

to be equivalent if they produce the same external effect

when applied in turn to a given body.

Resultant of force system (равнодействующая системы сил)
If a force system is equivalent to only single force, this force is called a resultant.

system to which the original system can be reduced.

The process

of reducing a force system to a simpler equivalent system is called composition (приведение).

The process of expanding a force or a force system into a less simple equivalent system is called resolution (разложение на составные части) .

A component (компонента) of a force is one of the two or more forces into which the given force may be resolved.

сил эквивалентная нулю)
A system of forces is called balanced if

the force system resultant is zero.



A rigid body under the action of balanced force system is in the state of equilibrium, i.e. body is at the rest or moves translational with uniform velocity along straight line.

acted upon by two forces will be in equilibrium if

and only if the two forces have the same magnitude and the same line of action but opposite sense.

a rigid body remains unchanged if another balanced force system

is added to, or subtracted from, the original system. In a special case, in accordance with Axiom 1, this balanced force system can consist of two equal and opposite forces acting along the common line .
It follows from Axiom 2 (corollary) that a force may be applied at any point on its given line of action without altering the resultant effects of the force, external to the rigid body on which it acts. The corollary is named the principle of transmissibility.

along force’s line of action without change to the state

of the body.
Force is sliding vector.

Без изменения состояния тела
точка приложения силы может быть перемещена вдоль линии действия силы.
Сила – скользящий вектор

of a body have as their resultant a force applied

at the same point and represented by the diagonal of a parallelogram constructed with the two given forces as its sides .

action and reaction existing between contacting bodies are equal in

magnitude and act along the same line in opposite directions

is in the state of static equilibrium, it would also

be in static equilibrium if the body were rigid.

forces a body is in the state of equilibrium therefore

lines of action of these forces are intersected at a common point, i.e. the force system is concurrent.