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Analytical Mechanics, 6 credits
Analytisk mekanik, 6 hp
TFYA40
Main field of study
Mathematics Applied Mathematics Applied Physics PhysicsCourse level
Second cycleCourse type
Programme courseExaminer
Iryna YakymenkoDirector of studies or equivalent
Magnus JohanssonEducation components
Preliminary scheduled hours: 56 hRecommended self-study hours: 104 h
Available for exchange students
YesECV = Elective / Compulsory / Voluntary
Main field of study
Mathematics, Applied Mathematics, Applied Physics, PhysicsCourse level
Second cycleAdvancement level
A1XCourse offered for
- Physics and Nanoscience, Master's Programme
- Physics and Nanotechnology
- Applied Physics and Electrical Engineering - International, M Sc in Engineering
- Applied Physics and Electrical Engineering, M Sc in Engineering
- Materials Science and Nanotechnology, Master's programme
Entry requirements
Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshold requirements for progression within the programme, or corresponding.
Prerequisites
Modern Physics, MechanicsIntended learning outcomes
The course represents the basic principles of classical mechanics within the framework of the variational approach. The knowledge of these principles is necessary for a deeper penetration into the structure of the classical mechanics itself, and also for a proper understanding of statistical mechanics, quantum mechanics etc. Furthermore, the methods of the analytical mechanics can serve as a set of the efficient tools for the solution of the majority of hard problems of mechanics and related topics.
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To achieve this aim students should be able to
- formulate the Lagrangian function for different mechanical systems,
- solve and analyze Lagrange's equations of motion for the set of generalized coordinates,
- formulate the Hamiltonian function for different mechanical systems,
- solve Hamiltion's equations of motion for the canonical variables,
- use the generating functions to make canonical transformations.
Course content
The variational approach to mechanics, Hamilton's principle, Lagrange's equations, first integrals and conservation theorems, elimination of cyclic variables, small oscillations theory, central force problem, Hamiltonian formulation of mechanics, canonical transformations, Hamilton-Jacobi theory,Poisson bracket formulation, introduction to analytical mechanics of continuous systems.
Teaching and working methods
Lectures and seminars with the solution of problems
Examination
| TEN1 | Written Examination | 6 credits | U, 3, 4, 5 |
Grades
Four-grade scale, LiU, U, 3, 4, 5Other information
Supplementary courses: Quantum Mechanics can be followed in parallel, Quantum Dynamic
Department
Institutionen för fysik, kemi och biologiDirector of Studies or equivalent
Magnus JohanssonExaminer
Iryna YakymenkoCourse website and other links
http://www.ifm.liu.se/undergrad/fysikgtu/coursepage.html?selection=all&sort=kkEducation components
Preliminary scheduled hours: 56 hRecommended self-study hours: 104 h
Course literature
Additional literature
Books
- H. Goldstein, Ch. Poole, J. Safko, (2001) Classical Mechanics 3
(selected parts). Addison & Wesley
Compendia
- I.I. Yakymenko, Lecture Notes in Analytical Mechanics
- I.I. Yakymenko, Set of Problems in Analytical Mechanics
| Code | Name | Scope | Grading scale |
|---|---|---|---|
| TEN1 | Written Examination | 6 credits | U, 3, 4, 5 |
Regulations (apply to LiU in its entirety)
The university is a government agency whose operations are regulated by legislation and ordinances, which include the Higher Education Act and the Higher Education Ordinance. In addition to legislation and ordinances, operations are subject to several policy documents. The Linköping University rule book collects currently valid decisions of a regulatory nature taken by the university board, the vice-chancellor and faculty/department boards.
LiU’s rule book for education at first-cycle and second-cycle levels is available at http://styrdokument.liu.se/Regelsamling/Innehall/Utbildning_pa_grund-_och_avancerad_niva.
Additional literature
Books
H. Goldstein, Ch. Poole, J. Safko, (2001) Classical Mechanics 3
(selected parts). Addison & Wesley
Compendia
I.I. Yakymenko, Lecture Notes in Analytical Mechanics
I.I. Yakymenko, Set of Problems in Analytical Mechanics
Note: The course matrix might contain more information in Swedish.
I = Introduce, U = Teach, A = Utilize
| I | U | A | Modules | Comment | ||
|---|---|---|---|---|---|---|
| 1. DISCIPLINARY KNOWLEDGE AND REASONING | ||||||
| 1.1 Knowledge of underlying mathematics and science (G1X level) |
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X
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X
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TEN1
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| 1.2 Fundamental engineering knowledge (G1X level) |
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| 1.3 Further knowledge, methods, and tools in one or several subjects in engineering or natural science (G2X level) |
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| 1.4 Advanced knowledge, methods, and tools in one or several subjects in engineering or natural sciences (A1X level) |
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| 1.5 Insight into current research and development work |
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| 2. PERSONAL AND PROFESSIONAL SKILLS AND ATTRIBUTES | ||||||
| 2.1 Analytical reasoning and problem solving |
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X
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TEN1
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| 2.2 Experimentation, investigation, and knowledge discovery |
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| 2.3 System thinking |
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| 2.4 Attitudes, thought, and learning |
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X
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| 2.5 Ethics, equity, and other responsibilities |
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| 3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION | ||||||
| 3.1 Teamwork |
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X
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| 3.2 Communications |
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X
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TEN1
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| 3.3 Communication in foreign languages |
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X
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X
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| 4. CONCEIVING, DESIGNING, IMPLEMENTING AND OPERATING SYSTEMS IN THE ENTERPRISE, SOCIETAL AND ENVIRONMENTAL CONTEXT | ||||||
| 4.1 External, societal, and environmental context |
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| 4.2 Enterprise and business context |
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| 4.3 Conceiving, system engineering and management |
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| 4.4 Designing |
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| 4.5 Implementing |
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| 4.6 Operating |
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| 5. PLANNING, EXECUTION AND PRESENTATION OF RESEARCH DEVELOPMENT PROJECTS WITH RESPECT TO SCIENTIFIC AND SOCIETAL NEEDS AND REQUIREMENTS | ||||||
| 5.1 Societal conditions, including economic, social, and ecological aspects of sustainable development for knowledge development |
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| 5.2 Economic conditions for knowledge development |
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| 5.3 Identification of needs, structuring and planning of research or development projects |
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| 5.4 Execution of research or development projects |
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| 5.5 Presentation and evaluation of research or development projects |
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