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Course Description Course Name : Analytical Mechanics Course Code : FK-503 Course Type : Compulsory Level of Course : Second Cycle Year of Study : 1 Course Semester : Fall (16 Weeks) ECTS : 6 Name of Lecturer(s) : Asst.Prof.Dr. BERRİN ÖZDEMİR Learning Outcomes of the Course : Knows Newton laws Knows cartesian, polar, cylindrical and spherical coordinates Writes the equation of motion for a system of particles Understands the importance of center of mass motion Knows conservation laws Knows the conditions under which the linear momentum and energy are conserved Knows the definition of angular momentum and the conditions under which it is conserved Knows generalized coordinates knows how to obtain Lagrange equations using D´Alembert principle Knows the difference between Lagrange method and Newton method Solves problems using the Lagrange method Knows how to obtain Lagrange´s equations of motion using variational principle Knows what central force is Obtains the equations of motion of a system under a central force Knows what rigid body is Knows Euler´s angles Knows the variation of a vector with time Knows Coriolis force Knows how to study small oscillation problems Mode of Delivery : Face-to-Face Prerequisites and Co-Prerequisites : None Recommended Optional Programme Components : None Aim(s) of Course : To investigate and compare the mechanics of a particle or system by Newton and Lagrange methods. To understand the importance and the difference of Lagrange method form the others. To understand the importance of mathematical formalism in the solution of physical problems. Course Contents : Variational principles and Lagrange´s Equations; Two-body Central force problems; rigid body equations of motion; Hamilton equations; canonical transformations; Hamilton - Jacobi theory; small oscillations. Language of Instruction : English Work Place : Lecture halls of faculty   Course Outline /Schedule (Weekly) Planned Learning Activities Week Subject Student's Preliminary Work Learning Activities and Teaching Methods 1 A general review of fundamental principles Research the related topic Lecture, discussion 2 Coordinate systems (Cartesian, polar, cylindrical, spherical) Research the related topic Lecture, discussion 3 Generalized coordinates and constraint conditions Research the related topic Lecture, discussion 4 D´Alembert principle and Lagrange´s equation Research the related topic Lecture, discussion 5 Problem solving with Lagrange´s method Research the related topic Lecture, discussion 6 Velocity dependent potential and the dissipation function Research the related topic Lecture, discussion 7 Variational principle and Lagrange´s equations of motion Research the related topic Lecture, discussion 8 Mid-term Examination Midterm Exam Midterm Exam 9 Lagrange equations for Holonomic and non-holonomic constraints Research the related topic Lecture, discussion 10 Conservation laws and symmetry Research the related topic Lecture, discussion 11 Central force and two body problem Research the related topic Lecture, discussion 12 Conservation laws of the systems moving under a central force Research the related topic Lecture, discussion 13 Kepler´s laws Research the related topic Lecture, discussion 14 Rigid body motion, Euler´s angles Research the related topic Lecture, discussion 15 Small oscillations Research the related topic Lecture, discussion 16/17 Final exam Final exam Final exam   Required Course Resources Resource Type Resource Name Recommended Course Material(s)  Classical Dynamics, H. Goldstein  Classical Dynamics of Particles and Systems, Marion, Thornton Required Course Material(s)   Assessment Methods and Assessment Criteria Semester/Year Assessments Number Contribution Percentage     Mid-term Exams (Written, Oral, etc.) 1 80     Homeworks/Projects/Others 1 20 Total 100 Rate of Semester/Year Assessments to Success 40   Final Assessments 100 Rate of Final Assessments to Success 60 Total 100   Contribution of the Course to Key Learning Outcomes # Key Learning Outcome Contribution* 1 Develop and deepen the knowledge as a specialist in physics or different areas based on the Physics Bachelor´s qualification level. 5 2 Comprehend the importance of multidisciplinary studies related to Physics. 5 3 Use his/her advanced theoretical and practical knowledge in Physics efficiently. 5 4 Integrate and interpret the knowledge from different disciplines with the help of his professional knowledge in Physics and conceptualize new perspectives. 5 5 Solve the problems in Physics by using research methods. 5 6 Carry out a study requiring expertise in physics independently. 5 7 Develop and provide new strategic approaches by taking responsibilty while solving the unexpected problems in Physics . 5 8 Take the responsibility of being the leader while solving the problems related to physical environments. 5 9 Evaluate the knowledge and skills gained in Physics by having a critical view and directs his/her learning. 5 10 Systematically transfer the current developments in the field of physics and his/her work to the person in physics field or outside of the field by supporting qualitative and quantitative data. 5 11 Take action to change the norms of social relations and critically examine these relationships, and develop them if necessary. 5 12 Make communication in oral and written by using at least one foreign language in the level of European Language Portfolio B2 level. 5 13 Use information and communication technologies in advanced level and use the software related with physics area. 5 14 Oversee social, scientific, cultural and ethical values in order to collect, implement, interpret data in Physics. 5 15 Develop strategies, policies and implementation plans in the issues related to the field of physics and evaluate the results obtained within the framework of quality processes. 5 16 Use the knowledge, problem solving, and / or practical skills obtained in the Physics Field in interdisciplinary studies. 5 * Contribution levels are between 0 (not) and 5 (maximum).   Student Workload - ECTS Works Number Time (Hour) Total Workload (Hour) Course Related Works     Class Time (Exam weeks are excluded) 14 4 56     Out of Class Study (Preliminary Work, Practice) 14 4 56 Assesment Related Works     Homeworks, Projects, Others 1 10 10     Mid-term Exams (Written, Oral, etc.) 1 14 14     Final Exam 1 14 14 Total Workload: 150 Total Workload / 25 (h): 6 ECTS Credit: 6