Analytical Mechanics, 6 credits

Analytisk mekanik, 6 hp

TFYA40

Main field of study

Mathematics Applied Mathematics Applied Physics Physics

Course level

Second cycle

Course type

Programme course

Examiner

Iryna Yakymenko

Director of studies or equivalent

Magnus Johansson

Education components

Preliminary scheduled hours: 56 h
Recommended self-study hours: 104 h

Available for exchange students

Yes
ECV = Elective / Compulsory / Voluntary
Course offered for Semester Period Timetable module Language Campus ECV
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 7 (Autumn 2017) 1 4 English Linköping E
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 7 (Autumn 2017) 1 4 English Linköping E
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 7 (Autumn 2017) 1 4 English Linköping E
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 7 (Autumn 2017) 1 4 English Linköping E
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 7 (Autumn 2017) 1 4 English Linköping E
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Applied Mathematics) 7 (Autumn 2017) 1 4 English Linköping E
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Applied Mathematics) 7 (Autumn 2017) 1 4 English Linköping E
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Applied Mathematics) 7 (Autumn 2017) 1 4 English Linköping E
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Applied Mathematics) 7 (Autumn 2017) 1 4 English Linköping E
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Applied Mathematics) 7 (Autumn 2017) 1 4 English Linköping E
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Materials and Nano Physics) 7 (Autumn 2017) 1 4 English Linköping E
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Materials and Nano Physics) 7 (Autumn 2017) 1 4 English Linköping E
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Materials and Nano Physics) 7 (Autumn 2017) 1 4 English Linköping E
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Materials and Nano Physics) 7 (Autumn 2017) 1 4 English Linköping E
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Materials and Nano Physics) 7 (Autumn 2017) 1 4 English Linköping E
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Mechatronics) 9 (Autumn 2017) 1 4 English Linköping E
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Mechatronics) 9 (Autumn 2017) 1 4 English Linköping E
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Mechatronics) 9 (Autumn 2017) 1 4 English Linköping E
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Mechatronics) 9 (Autumn 2017) 1 4 English Linköping E
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Mechatronics) 9 (Autumn 2017) 1 4 English Linköping E
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Theory, Modelling and Visualization) 7 (Autumn 2017) 1 4 English Linköping C
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Theory, Modelling and Visualization) 7 (Autumn 2017) 1 4 English Linköping C
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Theory, Modelling and Visualization) 7 (Autumn 2017) 1 4 English Linköping C
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Theory, Modelling and Visualization) 7 (Autumn 2017) 1 4 English Linköping C
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Theory, Modelling and Visualization) 7 (Autumn 2017) 1 4 English Linköping C
6CYYY Applied Physics and Electrical Engineering, M Sc in Engineering 7 (Autumn 2017) 1 4 English Linköping E
6CYYY Applied Physics and Electrical Engineering, M Sc in Engineering (Applied Mathematics) 7 (Autumn 2017) 1 4 English Linköping E
6CYYY Applied Physics and Electrical Engineering, M Sc in Engineering (Materials and Nano Physics) 7 (Autumn 2017) 1 4 English Linköping E
6CYYY Applied Physics and Electrical Engineering, M Sc in Engineering (Mechatronics) 9 (Autumn 2017) 1 4 English Linköping E
6CYYY Applied Physics and Electrical Engineering, M Sc in Engineering (Theory, Modelling and Visualization) 7 (Autumn 2017) 1 4 English Linköping C
6MMSN Materials Science and Nanotechnology, Master's programme 3 (Autumn 2017) 1 4 English Linköping E
6MFYS Physics and Nanoscience, Master's Programme 1 (Autumn 2017) 1 4 English Linköping E
6MFYS Physics and Nanoscience, Master's Programme (Experimentell fysik) 1 (Autumn 2017) 1 4 English Linköping E
6MFYS Physics and Nanoscience, Master's Programme (Teoretisk fysik) 1 (Autumn 2017) 1 4 English Linköping E
6KFYN Physics and Nanotechnology 5 (Autumn 2017) 1 4 English Linköping E

Main field of study

Mathematics, Applied Mathematics, Applied Physics, Physics

Course level

Second cycle

Advancement level

A1X

Course offered for

  • Physics and Nanotechnology
  • Physics and Nanoscience, Master's Programme
  • 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, Mechanics

Intended 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.

    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

TEN1Written Examination6 creditsU, 3, 4, 5

Grades

Four-grade scale, LiU, U, 3, 4, 5

Other information

Supplementary courses: Quantum Mechanics can be followed in parallel, Quantum Dynamic

Department

Institutionen för fysik, kemi och biologi

Director of Studies or equivalent

Magnus Johansson

Examiner

Iryna Yakymenko

Course website and other links

http://www.ifm.liu.se/undergrad/fysikgtu/coursepage.html?selection=all&sort=kk

Education components

Preliminary scheduled hours: 56 h
Recommended 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)
X
X
TEN1

                            
1.2 Fundamental engineering knowledge (G1X level)

                            
1.3 Further knowledge, methods, and tools in one or several subjects in engineering or natural science (G2X level)

                            
1.4 Advanced knowledge, methods, and tools in one or several subjects in engineering or natural sciences (A1X level)

                            
1.5 Insight into current research and development work

                            
2. PERSONAL AND PROFESSIONAL SKILLS AND ATTRIBUTES
2.1 Analytical reasoning and problem solving
X
TEN1

                            
2.2 Experimentation, investigation, and knowledge discovery

                            
2.3 System thinking

                            
2.4 Attitudes, thought, and learning
X

                            
2.5 Ethics, equity, and other responsibilities

                            
3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION
3.1 Teamwork
X

                            
3.2 Communications
X
TEN1

                            
3.3 Communication in foreign languages
X
X

                            
4. CONCEIVING, DESIGNING, IMPLEMENTING AND OPERATING SYSTEMS IN THE ENTERPRISE, SOCIETAL AND ENVIRONMENTAL CONTEXT
4.1 External, societal, and environmental context

                            
4.2 Enterprise and business context

                            
4.3 Conceiving, system engineering and management

                            
4.4 Designing

                            
4.5 Implementing

                            
4.6 Operating

                            
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

                            
5.2 Economic conditions for knowledge development

                            
5.3 Identification of needs, structuring and planning of research or development projects

                            
5.4 Execution of research or development projects

                            
5.5 Presentation and evaluation of research or development projects

                            

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