Elements of Theoretical Mechanics 390-FS1-2EMT
Educational profile: general academic.
Type of the studies: full-time.
Block (unit): theoretical physics, mandatory subject.
Field of knowledge and discipline of science: physical science, classical mechanics.
Elements of Classical Mechanics are the one-semester course of the subject. It includes 45 hours of the lecture and 45 hours of the discussion session (3 hours of the lecture and 3 hours of the discussion session per a week).
Balance sheet of the student's work: lecture (45 hours), practical (45 hours), consultations (15 hours), unassisted studying (105 hours).
Quantitative indicators:
- lecture and practical: 4,8 ECTS points
- unassisted studying: 4,2 ECTS points
The SI use is allowed for the translations, the bibliography preparing and computer modeling. The SI is forbidden during the colloquiums and the examination periods.
The goal of this course is to introduce the Lagrangian and Hamiltonian formulations of classical mechanics, as well as to discuss the basic applications of these formalisms to the description of the dynamics of systems of point masses and rigid bodies.
Lecture topics:
Newton's laws of dynamics
Conservative forces and energy
One-dimensional systems
Constraints and the principle of virtual work
d'Alembert's principle
Lagrange equations
Variational calculus
Hamilton's principle
The two-body principle
Small oscillations
Rigid body dynamics
The goal of the tutorials is for the students to acquire practial experience and expertise in analysing the motion of classical mechanical systems and developing a modest level of computational proficiency.
Topics discussed:
Review of selected topics in mathematical analysis
Conservative forces and energy
Constraints and generalized coordinates
Finding Lagrangians
Variational calculus and Lagrange equations
Hamilton's principle
Conservation laws and Noether's Theorem
The two-body problem
Small oscillations
Rigid body dynamics
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Term 2025:
None |
Term 2026:
Educational profile: general academic. Elements of Classical Mechanics are the one-semester course of the subject. It includes 45 hours of the lecture and 45 hours of the discussion session (3 hours of the lecture and 3 hours of the discussion session per a week). Balance sheet of the student's work: lecture (45 hours), practical (45 hours), consultations (15 hours), unassisted studying (105 hours). Quantitative indicators: The SI use is allowed for the translations, the bibliography preparing and computer modeling. The SI is forbidden during the colloquiums and the examination periods. The goal of this course is to introduce the Lagrangian and Hamiltonian formulations of classical mechanics, as well as to discuss the basic applications of these formalisms to the description of the dynamics of systems of point masses and rigid bodies. Lecture topics: The goal of the tutorials is for the students to acquire practial experience and expertise in analysing the motion of classical mechanical systems and developing a modest level of computational proficiency. Topics discussed: Review of selected topics in mathematical analysis |
Prerequisites (description)
Course coordinators
Term 2024: | Term 2025: | Term 2026: | Term 2023: |
Type of course
Mode
Number of hours of remote classes
Learning outcomes
Labels:
KP6_WG1, KP6_WG2, KP6_UW1, KP6_UK1, KP6_UK2, KP6_UU1, KP6_KK1, KP6_KK3, KP6_KK5, KP6_KO2
The student understands the notions of: the relativity of motion, reference frame, constraints, forces of reaction, virtual displacements, generalized coordinates. The students is able to introduce generalized coordinates, find the lagrangian and the hamiltonian, and work out the equations of motion. In some cases the student is able to solve these equations and analyse the result.
The student understands the role, origin and meaning of conservation laws and their relation to symmetries.
The student is able to find equilibria of mechanical systems and analyse small oscillations about them; understands the origin of Kepler's laws and the description of planetary orbits; has mastered the basics of classical mechanics to a degree which constitutes a good foundation for future studies.
The SI use is allowed for the translations, the bibliography preparing and computer modeling. The SI is forbidden during the colloquiums and the examination periods.
Assessment criteria
Written and oral examination. The student has to demonstrate both a command of the theory as well as the ability to solve simple problems.
The SI use is allowed for the translations, the bibliography preparing and computer modeling. The SI is forbidden during the colloquiums and the examination periods.
Assessment scale:
very good 5 (100%- 91%
good plus- 4,5 (90% -81%)
good 4 - (80% - 71%)
sufficient plus - 3,5 (70% - 61%)
sufficient 3 - (60% -51%)
insufficient 2 (50% - 0%)
Bibliography
Obligatory:
John R. Taylor, Classical Mechanics (2 volumes)
Suplemental:
L. Landau i E. Lifszyc, Mechanics
H. Goldstein, Theoretical Mechanics
G. L. Kotkin, W.G. Serbo, Problems in classical mechanics
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Term 2025:
None |
Additional information
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: