COURSE INTRODUCTION AND APPLICATION INFORMATION

Course Name
Analytical Mechanics
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
PHYS 309
Fall/Spring
2
2
3
5
Prerequisites
None
Course Language
English
Course Type
Elective
Course Level
First Cycle
Mode of Delivery -
Teaching Methods and Techniques of the Course
Course Coordinator
Course Lecturer(s)
Assistant(s) -
Course Objectives The aim of this class is to introduce classical mechanics in a new mathematically more advanced perspective so called LAgrange and Hamiltonian picture so that it will be usefull to connect classic mechanic to Quantum Mechanic.
Learning Outcomes The students who succeeded in this course;
  • Able to write down Lagrangian for any mechanical system
  • Adding conservation laws and constraints to the final lagrange equation
  • Using variational methods or directly they will be able to solve numerically or directly these equations
  • Using Legendre transformation they will obtain Hamiltonian equations fort he same problem.
  • Using Hamiltonian-Jacobi theory they wıll able to solve and compare to quantum mechanical equations.
Course Description A new perspective for classical mechanics which is easier to connect to quantum mechanics will be introduced using advance mathematical techniques and some example problems will be solved using these techniques.
Related Sustainable Development Goals

 



Course Category

 Core Courses
Major Area Courses
X
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Required Materials
1 Lagrange equation, constraints and general coordinates. Theoretical Physics 2: Analitical Mechanics. Wolfgang Nolting Bölüm 1.1
2 Friction, Non-holonomic systems. Theoretical Physics 2: Analitical Mechanics. Wolfgang Nolting Bölüm 1.2
3 Hamilton principal Theoretical Physics 2: Analitical Mechanics. Wolfgang Nolting Bölüm 1.3
4 Conservation Laws Theoretical Physics 2: Analitical Mechanics. Wolfgang Nolting Bölüm 1.4
5 Hamilton approach, legendre transformations Theoretical Physics 2: Analitical Mechanics. Wolfgang Nolting Bölüm 2.1
6 Canonical motion Theoretical Physics 2: Analitical Mechanics. Wolfgang Nolting Bölüm2.2
7 Action principal Theoretical Physics 2: Analitical Mechanics. Wolfgang Nolting Bölüm 2.3
8 Review of subjects till here. Theoretical Physics 2: Analitical Mechanics. Wolfgang Nolting Bölüm 1-2
9 Poisson brackets Theoretical Physics 2: Analitical Mechanics. Wolfgang Nolting Bölüm 2.4
10 Canonical transformations. Theoretical Physics 2: Analitical Mechanics. Wolfgang Nolting Bölüm 2.5
11 Hamilton-Jacobi equation Theoretical Physics 2: Analitical Mechanics. Wolfgang Nolting Bölüm 3.1
12 Solution methods Theoretical Physics 2: Analitical Mechanics. Wolfgang Nolting Bölüm 3.2
13 Action-angle coordinates Theoretical Physics 2: Analitical Mechanics. Wolfgang Nolting Bölüm 3.5
14 Connection to quantum mechanics. Theoretical Physics 2: Analitical Mechanics. Wolfgang Nolting Bölüm 3.6
15 General review Theoretical Physics 2: Analitical Mechanics. Wolfgang Nolting Bölüm 1-3
16 Final Exam
Course Notes/Textbooks

Theoretical Physics 2: Analitical Mechanics. Wolfgang Nolting
Suggested Readings/Materials

Classical Mechanics 3rd ed., H., Goldstein, Poole, Safko

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
1
10
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
5
10
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterm
2
40
Final Exam
1
40
Total

Weighting of Semester Activities on the Final Grade
8
60
Weighting of End-of-Semester Activities on the Final Grade
1
40
Total

ECTS / WORKLOAD TABLE

Semester Activities Number Duration (Hours) Workload
Course Hours
(Including exam week: 16 x total hours)
16
2
32
Laboratory / Application Hours
(Including exam week: 16 x total hours)
16
2
Study Hours Out of Class
1
36
36
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
2
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterms
2
20
Final Exams
1
10
    Total
150

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
 Program Competencies/Outcomes
* Contribution Level
1
2
3
4
5
1

To be able master and use fundamental phenomenological and applied physical laws and applications,

 X
2

To be able to identify the problems, analyze them and produce solutions based on scientific method,

 X
3

To be able to collect necessary knowledge, able to model and self-improve in almost any area where physics is applicable and able to criticize and reestablish his/her developed models and solutions,

 X
4

To be able to communicate his/her theoretical and technical knowledge both in detail to the experts and in a simple and understandable manner to the non-experts comfortably,

 X
5

To be familiar with software used in area of physics extensively and able to actively use at least one of the advanced level programs in European Computer Usage License,

 X
6

To be able to develop and apply projects in accordance with sensitivities of society and behave according to societies, scientific and ethical values in every stage of the project that he/she is part in,
7

To be able to evaluate every all stages effectively bestowed with universal knowledge and consciousness and has the necessary consciousness in the subject of quality governance,
8

To be able to master abstract ideas, to be able to connect with concreate events and carry out solutions, devising experiments and collecting data, to be able to analyze and comment the results,

 X
9

To be able to refresh his/her gained knowledge and capabilities lifelong, have the consciousness to learn in his/her whole life,

 X
10

To be able to conduct a study both solo and in a group, to be effective actively in every all stages of independent study, join in decision making stage, able to plan and conduct using time effectively.
11

To be able to collect data in the areas of Physics and communicate with colleagues in a foreign language ("European Language Portfolio Global Scale", Level B1).

 X
12

To be able to speak a second foreign at a medium level of fluency efficiently
13

To be able to relate the knowledge accumulated throughout the human history to their field of expertise.

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest