Course Information
SemesterCourse Unit CodeCourse Unit TitleL+PCreditNumber of ECTS Credits

Course Details
Language of Instruction English
Level of Course Unit First Cycle
Department / Program PHYSICS
Mode of Delivery Face to Face
Type of Course Unit Compulsory
Objectives of the Course To teach Lagrange and Hamilton formulations (that are used to study complicated mechanical and other dynamical systems, and are employed in modern physics) and to teach the relation between them. To study central forces , and to apply the results to study the kinematics of the solar system. To study many particle systems, to emphasize the center of mass concept and the conservation theorems. To derive the form of Newton s laws in non-inertial coordinates systems in the light of the fact that there are no true inertial frames in nature, and to study centrifugal and Coriolis forces. To teach rigid body dynamics in sufficient detail and depth.
Course Content Langrangian formulation, D’Alambert principle and Langrangian for a system. Hamiltonian, Legendre transformations. Hamilton’s equations of motion. Canonical transformations. Vibrations and stability.
Course Methods and Techniques
Prerequisites and co-requisities ( PHYS203 )
Course Coordinator None
Name of Lecturers Associate Prof.Dr. ENVER TARHAN
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources J.B. Marion, S.T. Thornton, "Classical Dynamics of particles and systems", Saunders College Pub., 1995
Classical Mechanics, T.W.B. Kibble, F.H. Berkshire Prentice-Hall, 1996
Theoretical Mechanics, T.C. Bradbury, John Willey & Sons, 1968.

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 % 25
Quizzes 0 % 0
Homeworks 2 % 25
Other activities 0 % 0
Laboratory works 0 % 0
Projects 0 % 0
Final examination 1 % 50
% 100

ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Weekly Course Time 14 3 42
Outside Activities About Course (Attendance, Presentation, Midterm exam,Final exam, Quiz etc.) 14 7 98
Application (Homework, Reading, Self Study etc.) 5 2 10
Exams and Exam Preparations 3 10 30
Total Work Load   Number of ECTS Credits 6 180

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 To be able to use Lagrangian formulation to write equations of motion. To be able to write the Hamiltonian for a given system, and to be able to solve equations of motion by using Hamiltonian formulation for simple systems, to regocnize the importance of Lagrange and Hamilton formulations for study of more diffiuclt systems and for study of conservations laws.
2 To be able to derive the Kepler s laws and to be able to apply them to planetary system by using the concepts of central forces, reduced mas, center of mass, conservation laws.
3 To be able to write Newton s laws in non-inertial coordinate frames, and to be able to apply these to the experimental value of gravitational constant, projectile motion, trade wind motions on the Earth.
4 To be able to apply Newton s laws, and the concepts of torque, angular momentum, moment of inertia, Euler angles to the motion of rigid bodies.

Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 Hamilton’s principle, generalized coordinates, Lagrange’s equations in generalized coordinates.
2 Equivalence of Lagrange’s and Newton’s equations, applications of Lagrange formulation.
3 Lagrange’s equations with undetermined multipliers, conservation theorems in Lagrange formulation
4 Hamiltonian formalism and Hamilton equations and their applications.
5 Central forces, reduced mass, conservation of angular momentum and Kepler’s second law.
6 Orbits in central field, centrifugal energy and the effective potential.
7 Planetary motion, Kepler’s third law, orbital dynamics and satellite launching.
8 Center of mass, linear momentum of a system of particles.
9 Angular momentum of the system, energy of the system.
10 Collision of two particles, cross section
11 Rotating coordinate systems, centrifugal and Coriolis forces.
12 Motion relative to the Earth.
13 Inertia tensor, angular momentum, principal axis of inertia.
14 Eulerian angles, Euler’s equations for a rigid body.

Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10
C1 4 4 4 2
C2 4 4 4 2
C3 4 4 4 2
C4 4 4 4 2

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