| TFYA40 |
Analytical Mechanics, 6 ECTS credits.
/Analytisk mekanik/
For:
FyN
MFYS
MSN
Y
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Prel. scheduled
hours: 56
Rec. self-study hours: 104
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Area of Education: Science
Main field of studies: Physics, Applied Physics, Mathematics, Applied Mathematics
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Advancement level
(G1, G2, A): A
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Aim:
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.
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Prerequisites: (valid for students admitted to programmes within which the course is offered)
Modern Physics, Mechanics
Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.
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Supplementary courses:
Quantum Mechanics can be followed in parallel, Quantum Dynamics
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Organisation:
Lectures and seminars with the solution of problems
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Course contents:
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.
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Course literature:
I.I. Yakymenko. Lecture Notes in Analytical Mechanics.
I.I. Yakymenko. Set of Problems in Analytical Mechanics.
H. Goldstein, Ch. Poole, J. Safko: Classical Mechanics, 3d edition (selected parts). Addison & Wesley, 2001.
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Examination: |
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A written examination with questions in theory and solution of problems (U,3,4,5)
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6 ECTS
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Course language is English.
Department offering the course: IFM.
Director of Studies: Magnus Johansson
Examiner: Iryna Yakymenko
Link to the course homepage at the department
Course Syllabus in Swedish
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