The discipline “Theoretical mechanics” is oriented on the studying by students of the theoretical foundations
of theoretical mechanics (statics, kinematics and dynamics).
It includes the consideration of the theoretical foundations of theoretical mechanics, statics, kinematics and dynamics,
and also directly the theoretical foundations of the resistance of materials and the details of machines.
The discipline has a practical direction on the formation of ability
to calculate the moment of physical force relative to the axis of rotation,
the center of gravity of the planar and volumetric geometrical figures,
the direction and nominal value of speed of the adjective, relative
and absolute motion of the material point, the physical force of inertia,
and also the value of its components, the longitudinal physical force and the normal mechanical stress,
the rotational mechanical moment of torque, stiffness and strength,
the axial, centrifugal and polar mechanical moment of inertia,
the mechanical construction for the strength and rigidity at bending,
the bar with a round cross section for the bending by twisting,
the mechanical construction for the fatigue at the uniaxial and simplified mechanical stress condition
and at the pure mechanical shear,
the critical physical force for the compressed bar of great flexibility,
and also the parameters of belt mechanical transmission and the checking and design parameters of the mechanical shaft.
The working program of the discipline “Theoretical mechanics” was developed
according to the acting educational standards and provides the training of diploma specialists
in the directions 651900 – “Automation and control” and 654700 – “Information systems”
in the specialties 210100 – “Control and informatics in the technical systems”
and 071900 – “Information systems and technologies”.
The discipline “Theoretical mechanics” is the foundation for the studying of the subsequent disciplines:
“Mechanical-engineering”, “The resistance of materials” and “Automation of technological processes and productions”.
The purposes and tasks of discipline:
1. The studying of the origin and development of classical theoretical mechanics.
2. The studying of the theoretical foundations of theoretical mechanics.
3. The studying of the theoretical foundations and features of statics.
4. The studying of the theoretical foundations and features of kinematics.
5. The studying of the theoretical foundations and features of dynamics.
6. The studying of the theoretical foundations and features of the resistance of materials.
7. The studying of the theoretical foundations and features of the details of machines.
According to requirements to the level of development of discipline students have to:
1. Know the genesis and tendences of development of the classical theoretical mechanics.
2. Be able to use the theoretical foundations of theoretical mechanics.
3. Be able to use the theoretical foundations of classical statics.
4. Have the idea about the theoretical foundations of classical kinematics.
5. Know the features of the theoretical foundations of classical dynamics.
6. Know the theoretical foundations and features of the resistance of materials.
7. Have the idea about the theoretical foundations and features of the details of machines.
The table of contents of the working program of the discipline “Theoretical mechanics”
The list of sections and themes of the discipline
The section 1. “The theoretical foundations of theoretical mechanics”.
The theme 1. “The short historical reference of the development of theoretical mechanics”.
Theoretical mechanics: the concept and place among the natural and technical sciences.
The genesis and the main historical stages of development of (theoretical) mechanics.
The section 2. “The theoretical foundations of statics”.
The theme 2. “The main concepts and axioms of statics”.
Statics: the concept and subject.
The main concepts of statics: the absolutely solid body, the physical force, the equivalent system of forces,
the equal force, the balanced system of forces, the external force and the internal force.
The main axioms of statics: the concept, appointment and classification.
The relationship: the concept, appointment and classification. The reaction of relationship: the concept and appointment.
The theme 3. “The flat system of converging physical forces”.
The ways of adding up of the physical forces: the concept, appointment and classification
(the geometric and analytical ways of adding up of the physical forces).
The converging physical force: the concept and appointment.
The equal physical force of converging forces: the concept and appointment.
The geometric condition of equilibrium of the system of converging physical forces.
The analytical (mathematical) conditions of the (geometric) equilibrium
of the flat and spatial system of physical forces.
The theme 4. “The flat system of mechanical pairs of the physical forces”.
The moment of physical force relative to the point of application (the center of gravity).
The mechanical pair of physical forces: the concept and appointment.
The moment of the mechanical pair of physical forces as the vector value.
The theorem about the sum (superposition) of the mechanical moments of physical forces,
forming the mechanical pair, relative to any center of gravity.
The theorem about the equivalence of mechanical pairs: the concept and appointment.
The addition of mechanical pairs, arbitrarily located in the space of coordinates.
The condition of equilibrium of the system of mechanical pairs of the physical forces.
The theme 5. “The arbitrary flat system of physical forces”.
The analytical (mathematical) quantity of the moment of physical force.
The calculation of the main vector and moment of the flat system of physical forces.
The analytical (mathematical) conditions of the flat system of physical forces:
the concept, appointment and classification (kinds) of the conditions of equilibrium.
The analytical conditions of equilibrium of the flat system of parallel physical forces.
The concentrated and distributed physical forces: the concept and appointment.
The physical forces, evenly distributed by the straight line and their equal-effect.
The theme 6. “The spatial system of physical forces”.
The moment of physical force relative to the axis of rotation.
The relationship between the moments of physical force relative to the center of gravity and the axis of rotation,
passing through the given center of gravity.
The analytical (mathematical) formulas for the providing of calculation
of the moments of physical force relative to three axes in the given system of coordinates.
The private cases of bringing of the spatial system of physical forces.
The theme 7. “The center of gravity of the physical (mechanical) bodies”.
The center of gravity of the parallel physical forces: the concept and appointment.
The analytical (mathematical) formulas for the determining of coordinates of the center of gravity
of the parallel physical forces of the various mechanical bodies.
The center of gravity of the solid mechanical body: the concept and appointment.
The features of coordinates of the centers of gravity of the homogeneous mechanical bodies
(the calculation of the center of gravity of the volume, square, line and point).
The features of calculation of the center of gravity of the simple geometric figures
(the calculation of the center of gravity of the arc of circle, triangle and the sector of circle).
The section 3. “The theoretical foundations of kinematics”.
The theme 8. “The main concepts of classical kinematics”.
Kinematics: the concept and subject. The space and time in the theoretical mechanics.
The relativity of mechanical motion: the concept and appointment.
The point of reference in the system of coordinates: the concept and appointment.
The system of coordinates: the concept, appointment and classification (kinds).
The main definitions and tasks of kinematics: the concept, appointment and classification.
The theme 9. “The main kinds of motion of the physical (mechanical) bodies”.
The translational mechanical motion of solid physical (mechanical) body:
the concept, appointment and main properties.
The rotational mechanical motion of solid physical (mechanical) body around the fixed axis:
the concept, appointment and properties.
The analytical (mathematical) equation of the rotational mechanical motion.
The average angular speed at the given moment of time: the concept and appointment.
The frequency of mechanical rotation: the concept and appointment.
The angular speed of mechanical rotation: the concept and the units of measurement.
The linear speed (acceleration) of material points at the rotation of mechanical body.
The theme 10. “The difficult motion of material point”.
The motion of material point: the concept, appointment and classification
(the transient, relative and absolute motion of material point).
The theorem about the addition of speeds at the difficult motion: the concept and appointment.
The theme 11. “The difficult motion of physical (mechanical) body”.
The plane-parallel motion of physical (mechanical) body: the concept and appointment.
The decomposition of plane-parallel motion: the concept and appointment.
The main ways of determining of the instantaneous center of speeds at the motion.
The section 4. “The theoretical foundations of dynamics”.
The theme 12. “The main concepts of classical dynamics”.
Dynamics: the concept, subject and the main tasks of dynamics.
The principle of inertia (the first axiom of dynamics): the concept and appointment.
The main law of dynamics of the material point (the second axiom of dynamics).
The physical mass of material point: the concept and appointment.
The relationship between the physical mass and the force of gravity in dynamics.
The law of independence of the action of physical forces (the third axiom of dynamics).
The law of equality of the action and opposition (the fourth axiom of dynamics).
The theme 13. “The features of the method of kinetic static”.
The free and non-free material point: the concept and appointment.
The physical force of inertia: the concept and appointment.
The physical force of inertia at the straight linear motion of material point.
The physical force of inertia at the curvilinear motion of material point.
The mathematical principle of D'Alembert J.L.: the concept and appointment.
The physical method of kinetic static: the concept and appointment.
The section 5. “The theoretical foundations of the resistance of materials”.
The theme 14. “The main theoretical provisions of the resistance of materials”.
The resistance of materials: the concept, appointment and classification
(the features of calculation of the strength, stiffness and stability).
The physical load: the concept, appointment and classification.
The main hypotheses and assumptions about the physical properties of deformable body.
The physical deformation: the concept, appointment, characteristics and classification.
The principle of independence of the action of physical forces: the concept and appointment.
The method sections: the concept, appointment and the features of application.
The application of the method of sections for the determining of the internal force factors,
occurring in the cross sections of the wood or metal bar.
The physical stress: the concept, appointment and classification (kinds)
(the full stress, the normal stress and the tangent stress).
The theme 15. “The calculation of mechanical connections on shearing and crushing”.
The physical (mechanical) slice: the concept, classification,
the main prerequisites and the mathematical formulas for the calculating of slice.
The physical (mechanical) crushing: the concept, conditions and mathematical formulas.
The mathematical calculations on shearing and crushing of the connections with rivets and bolts.
The theme 16. “The geometric characteristics of planar sections”.
The physical (mechanical) moment of inertia: the concept, appointment and classification
(the axial moment of inertia, the centrifugal moment of inertia and the polar moment of inertia).
The main geometric axis of rotation and the main physical moment of inertia.
The axial moment of inertia of the simplest sections: the concept, appointment and kinds
(the axial moment of inertia of the rectangle, circle and ring).
The theme 17. “The theoretical foundations of physical (mechanical) bend”.
The physical (mechanical) bend: the concept, appointment and classification.
The classification (kinds) of bends: the straight bend (clean and transverse).
The internal force factor of straight bend (the transverse force and bending moment).
The differential relationships between the bending moment,
the transverse physical force and the intensity of distributed load.
The drawing of diagrams of the transverse physical forces and bending moments.
The normal physical (mechanical) stress,
occurring in the cross section of the wood and metal bar at the clean bend.
The theme 18. “The theoretical foundations of physical (mechanical) stretching and bending of the bar”.
The calculation of bar with high stiffness at the joint bending and tension (compression).
The determination of the normal physical stress in the cross sections,
the finding of hazardous points and the calculation of the strength of construction.
The theme 19. “The theoretical foundations of physical (mechanical) resistance of fatigue”.
The physical (mechanical) fatigue failure: the concept, kinds and causes.
The physical (mechanical) limit of endurance: the concept and appointment.
The relationship of the physical (mechanical) limit of endurance
with the characteristics of static strength from the kind of the load of bar.
The dependence of the physical (mechanical) limit of endurance from the asymmetry.
The local physical stress and its impact on the limit of endurance.
The theme 20. “The foundations of physical (mechanical) stability of the compressed rod”.
The stable and unstable forms of elastic equilibrium: the concept and appointment.
The critical physical force: the concept, appointment and application.
The critical and permissible physical loads: the concept, features and relationship.
The ultimate flexibility: the concept and appointment. The calculation of stability of the compressed rod.
The section 6. “The theoretical foundations of the details of machines”.
The theme 21. “The main provisions of the theory of the details of machines”.
The theory of the details of machines: the genesis, the main concepts and appointment.
The modern tendences in the continuous development of mechanical-engineering.
The main requirements to the modern machines and their details.
The main criteria of workability and the calculation of the details of machines.
The features of selection of the various materials for the different details of machines.
The features of execution of the design and verification calculations of the details of machines.
The theme 22. “The general details about the physical (mechanical) transmission”.
The rotational motion: the concept, appointment and role in mechanisms and machines.
The physical (mechanical) transmission in machines: the concept, appointment and classification.
The main power and kinematic ratios in the mechanical transmission.
The theme 23. “The general details about the flat mechanisms and machines”.
The articulated four-link mechanism: the concept and appointment.
The crank-slider and link mechanisms: the concept and appointment.
The cam mechanism and machine: the concept and appointment.
The mechanism of intermittent motion: the concept and appointment.
The theme 24. “The general details about the friction mechanical transmission”.
The friction mechanical transmission: the concept, appointment, classification,
advantages, disadvantages and the features of application in mechanisms and systems.
The coefficient of useful effect of the friction mechanical transmission.
The kinds of fracture of the working surface of the friction mechanical roller.
The characteristics of the friction mechanical transmission: the gear ratio and variators.
The theme 25. “The general details of the gear mechanical transmission”.
The gear mechanical transmission: the concept, appointment, classification,
advantages, disadvantages, the features of application in mechanisms and systems.
The main theories of gear engagement. The features of manufacturing of the gear wheel.
The features of materials and structure of the gear mechanical wheels.
The damage of the mechanical tooth: the concept, features and classification.
The main criteria of workability of the gear mechanical transmission.
The main geometric ratios of the gear mechanical transmission.
The theme 26. “The general details about the mechanical transmission "screw-nut"”.
The mechanical transmission "screw-nut": the concept, classification, appointment
and the features of application (the practical use).
The coefficient of useful effect and gear ratio of the mechanical transmission “screw-nut”.
The resolution of the mechanical transmission “screw-nut”: the concept, appointment and classification,
and also the materials of manufacturing of the mechanical screw pair.
The features and sequence of calculation of the parameters of the mechanical transmission “screw-nut”.
The allowable stress of the mechanical transmission “screw-nut”: the concept and calculation.
The theme 27. “The general details about the worm mechanical transmission”.
The worm mechanical transmission: the concept, appointment, classification,
advantages, disadvantages and the area of application (the practical use),
and also the materials of the manufacture of the mechanical worm and worm wheel.
The worm mechanical transmission with “Archimedean worm”:
the concept, appointment, application, the main geometric and kinematic relations.
The worm mechanical transmission with offset: the concept and appointment.
The main elements of structure of the worm mechanical transmission (with offset).
The features of calculation of the worm mechanical transmission and force in engagement.
The theme 28. “The general details about the belt mechanical transmission”.
The belt mechanical transmission: the concept, appointment, the principle of functioning,
structure, advantages, disadvantages and application (the practical use).
The main elements of structure of the belt mechanical transmission:
the mechanical drive belts, the mechanical pulleys and tensioning devices.
The comparative characteristic of parameters of the belt mechanical transmission
with the mechanical flat, wedge and poly-wedge belt.
The physical forces and mechanical stresses in the structure of mechanical belt.
The physical forces, acting on the mechanical shafts and bearings.
The features of sliding of the mechanical belt on the mechanical pulleys,
and also the gear ratio and the coefficient of useful effect of the construction.
The theme 29. “The general details about the chain mechanical transmission”.
The chain mechanical transmission: the concept, appointment, the principle of functioning,
structure, advantages, disadvantages and application (the practical use).
The main elements and details of the structure of the chain mechanical transmission:
the mechanical drive chain, the mechanical sprocket and tensioning device.
The main geometric relationships in the chain mechanical transmission,
and also the physical forces, acting in the chain mechanical transmission.
The theme 30. “The general details about the mechanical gearbox and variator”.
The mechanical gearbox: the concept, appointment, the principle of functioning,
the features of application and the ways of fixing of the mechanical shafts in the gearboxes.
The mechanical variator: the concept, appointment and the principle of functioning.
The theme 31. “The general details about the mechanical axis, shaft and connection”.
The mechanical axis: the concept, appointment, structure and the materials of manufacture.
The mechanical shaft: the concept, appointment, structure and the materials of manufacture.
The mechanical connection: the concept, appointment, structure and the materials of manufacture.
The features of calculation of the mechanical shaft and axis on strength and rigidity.
The main organizational, constructure and technological ways
of the increasing of endurance of the mechanical shaft and mechanical axis.
The spline mechanical connection: the concept, appointment and classification.
The calculation of mechanical connections with prismatic and segment splines.
The theme 32. “The general details about the mechanical bearing and clutch”.
The mechanical bearing of sliding: the concept, appointment,
structure, classification and application (the practical use).
The mechanical bearing of rolling: the concept, appointment,
structure, classification and application (the practical use).
The comparative characteristic of the mechanical bearings of rolling and sliding.
The mechanical clutch: the concept, appointment, structure,
classification and application (the practical use),
and also the features of selection and calculation.
The theme 33. “The general details about the threaded mechanical connection”.
The threaded mechanical connection: the concept, appointment,
structure, classification and application (the practical use).
The mechanical thread: the concept, appointment, structure, the geometric parameters,
classification and application (the practical use).
The main kinds of construction of the threaded mechanical connection,
and also its standard mechanical elements and fixing products.
The main ways of locking of the threaded mechanical connections.
The theme 34. “The general details about the welded, soldered and glued mechanical connection”.
The welded mechanical connection: the concept, appointment, classification,
advantages, disadvantages and application (the practical use).
The mechanical weld joint: the concept, appointment, classification (kinds),
advantages, disadvantages and application (the practical use).
The features of calculation of the welded mechanical connections end-to-end and overlapping
at the axial physical loading of the connected mechanical details.
The soldered mechanical connection: the concept, appointment, classification,
advantages, disadvantages and application (the practical use).
The adhesive mechanical connection: the concept, appointment, classification,
advantages, disadvantages and application (the practical use).
The list of laboratory works
on the discipline “Theoretical mechanics”
1. The calculation of the moment of physical force relative to the axis of rotation.
2. The calculation of the center of gravity of the planar and volumetric geometric shapes.
3. The calculation of the direction and nominal value of speed
of the transient, relative and absolute motion of the material point.
4. The calculation of the physical force of inertia, and also the values of its components.
5. The calculation of the longitudinal physical force and normal mechanical stress.
6. The calculation of the torsional mechanical moment of rotation, stiffness and strength.
7. The calculation of the axial, centrifugal and polar mechanical moment of inertia.
8. The calculation of the mechanical construction on strength and stiffness at bending.
9. The calculation of the bar with the circular cross section on bending by twisting.
10. The calculation of the mechanical construction on fatigue at the uniaxial and simplified
mechanical stress condition and at the pure mechanical shear.
11. The calculation of the critical physical force for the compressed bar of great flexibility.
12. The calculation of parameters of the belt mechanical transmission.
13. The calculation of the check and design parameters of the mechanical shaft.
The list of recommended literature
The basic sources
1. Akimov, V.A. Theoretical mechanics. Kinematics. Workshop: Learning manual /
V.A. Akimov, O.N. Sklyar, A.A. Feduta;
The common ed. by prof. A.V. Chigarev. – M.: “INFRA-M”, “New knowledge”, 2017. – 635 p.
2. Andreyev V.I. Technical mechanics (for the students of construction HEIs and faculties): Textbook /
V.I. Andreyev, A.G. Paushkin, A.N. Leontyev. – M.: “ACB”, 2016. – 256 p.
3. Butenin N.V. The course of theoretical mechanics: Textbook. In 2 volumes.
Volume 1: Static and kinematics. – the 4th ed., corr. – M.: “Science”, 1985. – 240 p.
4. Butenin N.V. The course of theoretical mechanics: Textbook. In 2 volumes.
Volume 2: Dynamics. – the 3rd ed., corr. – M.: “Science”, 1985. – 496 p.
5. Vas’ko N.G. Theoretical mechanics: Textbook /
N.G. Vas’ko, V.A. Volosukhin, A.N. Kabel’kov. – Ron/D: “Phoenix”, 2016. – 302 p.
6. Vereina L.I. Technical mechanics: Textbook for the average prof. education /
L.I. Vereina, M.M. Krasnov. – M.: “PC "Academy"”, 2016. – 352 p.
7. Olofinskaya V.P. Technical mechanics: The course of lectures with the variants of practical and test tasks:
Learning manual /V.P. Olofinskaya. – M.: “Forum”, 2016. – 352 p.
8. Polyakhov N.N. Theoretical mechanics: Textbook for the bachelors /
N.N. Polyakhov, S.A. Zegzhda, M.P. Yushkov; Ed. by P.E. Tovstick. – M.: “Yurite”, 2016. – 593 p.
9. Safonova G.G. Technical mechanics: Textbook /
G.G. Safonova, T.Yu. Artyukhovskaya, D.A. Ermakov. – M.: “SPC "INFRA-M"”, 2018. – 320 p.
10. Setkov V.I. Technical mechanics for the construction specialties:
Learning manual for the students of average prof. education /
V.I. Setkov. – M.: “PC "Academy"”, 2017. – 400 p.
11. Targ S.M. The short course of theoretical mechanics: Textbook for the HTEIs. –
the 12th ed. – M.: “Higher school”, 2002. – 416 p.
The additional sources
1. Atarov N.M. The resistance of materials in examples and tasks. –
M.: “Infra-M”, 2010. – 262 p.
2. Afanas’yev V.G. Theoretical mechanics. P.1. Statics and kinematics /
V.G. Afanas’yev, P.F. Sabodash. – M.: “MSUP”, 2011. – 158 p.
3. Afanas’yev V.G. Theoretical mechanics: Part 3. Dynamics: Learning-methodical manual /
V.G. Afanas’yev. – M.: “MSUP”, 2009. – 60 p.
4. Bat’ M.I. Theoretical mechanics in examples and tasks: Volume 1: Statics and kinematics /
M.I. Bat’, G.Yu. Dzhanelidze, A.S. Kel’zon. – the 8th ed., redesign. – M.: “Science”, 1984. – 504 p.
5. Bat’ M.I. Theoretical mechanics in examples and tasks:
Textbook for the HEIs in 3 volumes: Volume 2. Dynamics /
M.I. Bat’, G.Yu. Dzhanelidze, A.S. Kel’zon; ed. by Merkin D.R. –
the 7th ed., redesign. – Leningrad: “Publ.-house "Science"”, 1985. – 560 p.
6. Vardanyan G.S., Andreyev V.I., Atarov N.M., Gorshkov A.A.
The resistance of materials with the foundations of the theory of elasticity and plasticity. – M.: “Infra-M”, 2010. – 193 p.
7. Vardanyan G.S., Atarov N.M., Gorshkov A.A.
The resistance of materials with the foundations of construction equipment. – M.: “Infra-M”, 2010. – 124 p.
8. Vereina L.I. Technical mechanics. – M.: “Academy”. 2011. – 352 p.
9. Ksendzov V.A. Technical mechanics. – M.: “Kolos press”, 2010. – 291 p.
10. Lachuga Yu.F. Technical mechanics. – M.: “Kolos press”, 2010. – 376 p.
The list of questions for the preparation to the examination or automized testing
1. The list of examination questions (download).
2. The list of the themes of abstracts (for the students of the first course of day and evening departments) (download).
The planned schedule of theoretical course of lectures and laboratory practical work
on the discipline “Theoretical mechanics”
Day department: lectures and laboratory practical work
Evening department: lectures and laboratory practical work
According to the preliminary arrangement
