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Theoretical Mechanics I

Course developer

Prior knowledge

Fizi2032, Physics I

Mate1030, Mathematics II

MateB001, Mathematics I

Replaced course

Meha4008 [GMEH4008] Theoretical Mechanics I

Course abstract

The aim of the study course is to master the main basic principles of theoretical mechanics. Students learn the concept of force, methods of force calculation in static structures, methods of calculation of kinematic parameters of motion, develop logical thinking and form a knowledge base for the acquisition of technical disciplines.

Learning outcomes and their assessment

Knowledge - understands what is called strength and what is the moment of strength. Has an understanding of force addition by the projection method and is able to compile equilibrium equations. Has an understanding of how to determine the moment of force and is able to count them. Understands how to determine the conditions of motion in mechanics and is able to calculate (test).
Skills - is able to view in an abstract and analytical way the equilibrium state of various solid bodies and structures and the effect on other mechanical systems (independent works).
Competence - the ability to use the basic principles of theoretical mechanics in practical and scientific work, as well as in the invention and implementation of technically innovative processes (independent works).

Course Content(Calendar)

1. Introduction. Basic concepts of mechanic course. Static axiom. Vector algebra. (2h L; 2h PrD; 4h PstD) (Test 1 for 1st)
2. Strength. Addition of forces (vectors). (2h L; 2h PrD; 4h PstD);
3. In-plane force systems. (1h L, 2h PrD; 4h PstD)
4. In-plane distributed force systems (1h L, 2h PrD; 5h PstD); (Test 2 for 3rd, 4th)
5. Moment of force. Moment counting. (1h L, 2h PrD; 5h PstD);
6. Moment of force pair. Addition of force pair moments. (1h L, 2h PrD; 4h PstD); (3rd test for 5th, 6th);
7. Sliding friction. Rolling friction. Equilibrium of the body system with respect to friction. (1h L; 2h PrD; 4h PstD); (Test 4 on the 7th)
8. Body center of gravity. Stability. (1h L; 2h PrD; 4h PstD);
9. Techniques of point movement. Speed. Acceleration. Natural triedrs. (2h L; 2h PrD; 4h PstD) (Test 5 on 9.)
10. Rotational movement. Gear ratio. (1h L; 2h PrD; 6h PstD) (Test 6 on 10.)
11. Complex movement. Accelerating speeds. (2h L; 2h PrD; 8h PstD)
12. Movement in the complex. Accelerations in complete motion. (2h L; 2h PrD; 8h PstD) (Test 7 on 11., 12.)
13. Compound movement. Speeds and accelerations in compound motion. Acceleration of cariolis. (1h L, 2h PrD; 8h PstD); (Test 8 on 13.)

Part-time extramural studies:
All the topics intended for full-time studies are covered, yet the number of contact hours is ½ of the specified number of hours.

Requirements for awarding credit points

The exam is structured as follows (cumulative):
• all (eight) tests must be written successfully (at least 4 points);
• all correctly solved independent works are included.

Description of the organization and tasks of students’ independent work

Independent work - To solve theoretical problems of mechanics, in-depth study of the topics covered in lectures and perform independent work:
1. Independent work: Addition of vectors by projection method.
2. Independent work: Addition of forces of the system of connecting forces.
3. Independent work: Addition of forces and moments of a distributed force system.
4. Independent work: Determination of friction force.
5. Independent work: Determining the center of gravity of a figure's area.
6. Independent work: Movement of a point.
7. Independent work: Rotational movement.
8. Independent work: Speeds and accelerations in complete movement.
9. Independent work: Compound movement.

Criteria for Evaluating Learning Outcomes

The exam grade is formed cumulatively from tests and independent work.

Compulsory reading

1. Kabus K. Mechanik und Festigkeitslehre. 5 Auflage, München Wien: Carl Hanser Verlag, 2003. 276 S.
2. Muvdi B.B., Al-Khafaji A.W., McNabb J.W. Statics for Engineers. Bradley University, 1996.

3. Müller W.H., Ferber F. Technische Mechanik für Ingenieure. 4 aktualisierte Auflage. Fachbucherverlag Leipzig: Carl Hanser Verlag, 2011. 538 S.

Further reading

1. Kepe O.,Vība J. Teorētiskā mehānika. Rīga: Zvaigzne, 1982. 577 lpp.
2. Teorētiskā mehānika piemēros. O. Kepes redakcijā. Rīga: Zvaigzne, 1976. 647 lpp.
3. Teorētiskās mehānikas uzdevumi. O. Kepes un J. Vības red. 1.izd. Rīga: Zvaigzne, 1989. 479 lpp.

Periodicals and other sources

1. Szolga V. Theoretical Mechanics: lecture notes and sample problems. Part I: Statics and Kinematics. 2010. 203 p. [tiešsaiste] [skatīts 27.11.2023.]. Pieejams: https://docplayer.net/14931020-Theoretical-mechanics.html
2. Szolga V. Theoretical Mechanics: lecture notes and sample problems. Part II. Kinematics, Dynamics. 2010. 261 p. [tiešsaiste] [skatīts 27.11.2023.]. Pieejams: https://dokumen.tips/documents/theoretical-mechanics-facultatea-de-constructii-profdring-vasile-szolga.html?page=1

Notes

The study course is included in the Compulsory part of the Bachelor’s study program “Agricultural Engineering” and “ Machine design and Manufacturing”