Course Information
SemesterCourse Unit CodeCourse Unit TitleL+PCreditNumber of ECTS Credits
4MATH240ANALYTICAL MECHANICS3+036

Course Details
Language of Instruction English
Level of Course Unit First Cycle
Department / Program MATHEMATICS
Mode of Delivery Face to Face
Type of Course Unit Elective
Objectives of the Course To learn the basics of analytical mechanics
Course Content Geometry of motion. The Newton equations of motion. Generalized coordinates. Calculus of variations and the principle of least action. The Euler-Lagrange equations. Conservation laws. Energy. Momentum. Centre of mass. Angular momentum. Integration of the equations of motion. Motion in one dimension. The reduced mass. Motion in a central field. Small oscillations. Free oscillations in one dimension. Forced oscillations. Damped oscillations. The canonical equations. Hamilton’s equations.
Course Methods and Techniques
Prerequisites and co-requisities None
Course Coordinator None
Name of Lecturers Associate Prof.Dr. Fatih Erman
Prof.Dr. Oktay Pashaev
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources Classical Mechanics with Calculus of Variations and Optimal Control An Intuitive Introduction, Mark Levi, AMS
Classical Dynamics of Particles and Systems, S. T. Thornton, J. B. Marion

Course Category

Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"

Assessment Methods and Criteria
In-Term Studies Quantity Percentage
Midterm exams 2 % 50
Quizzes 4 % 20
Homeworks 0 % 0
Other activities 0 % 0
Laboratory works 0 % 0
Projects 0 % 0
Final examination 1 % 30
Total
7
% 100

ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Weekly Course Time 1 48 48
Outside Activities About Course (Attendance, Presentation, Midterm exam,Final exam, Quiz etc.) 1 47 47
Application (Homework, Reading, Self Study etc.) 1 0 0
Exams and Exam Preparations 2 48 96
Total Work Load   Number of ECTS Credits 6 191

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 Apply some techniques in linear algebra, calculus and differential equations to mechanical systems.
2 To able to solve some simple problems in Newtonian dynamics.
3 To understand the main problem of the calculus of variations, and to be able to solve some of its applications to geometry and mechanics.
4 To find Lagrangian for a given mechanical system and to find equations of motion using Euler-Lagrange equations.
5 To be able to find the Hamiltonian for a given mechanical system and find equations of motion using Hamilton's equations.
6 To be able to apply the Noether's theorem to mechanical systems.


Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 Geometry of motion. The Newton equations of motion
2 Generalized coordinates, examples.
3 Calculus of variations and the principle of least action.
4 The Euler-Lagrange equations.
5 Conservation laws. Energy and Momentum.
6 Midterm 1
7 Angular momentum, centre of mass..
8 Integration of the equations of motion. Motion in one dimension.
9 Integration of the equations of motion. Motion in one dimension.
10 The reduced mass. Motion in a central field.
11 Midterm 2
12 Small oscillations. Free oscillations in one dimension.
13 Forced oscillations. Damped oscillations.
14 The canonical equations. Hamilton’s equations.
15 The canonical equations. Hamilton’s equations.
16 Final Exam


Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14
C1 4 4 4
C2 4 4 4
C3 4 4 4
C4 4 4 4
C5 4 4 4
C6 4 4 4

Contribution: 0: Null 1:Slight 2:Moderate 3:Significant 4:Very Significant


https://obs.iyte.edu.tr/oibs/bologna/progCourseDetails.aspx?curCourse=254371&lang=en