• Basic information
• Learning outcomes
• Contents
• Assessment
• Workload

Learning outcomes

Upon successful completion of this course, students will be able to:

1. To write Euler-Lagrange equations on the tangent bundles, and to write Hamilton's equations on the cotangent bundles.

   Contribution to Program Outcomes

   1. Define and manipulate advanced concepts of Mathematics in a specialized way
   2. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
   3. Gain original, independent and critical thinking, and develop theoretical concepts and tools,
   4. Understand relevant research methodologies and techniques and their appropriate application within his/her research field,
   5. Question and find out innovative approaches.
   6. Acquire scientific knowledge and work independently,
   7. Effectively express his/her research ideas and findings both orally and in writing
   8. Be aware of issues relating to the rights of other researchers and of research subjects e.g. confidentiality, attribution, copyright, ethics, malpractice, ownership of data

   Method of assessment

   1. Written exam
   2. Homework assignment
2. To reduce Hamilton's equations on the cotangent bundle of a Lie group under symmetries.

   Contribution to Program Outcomes

   1. Define and manipulate advanced concepts of Mathematics in a specialized way
   2. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
   3. Gain original, independent and critical thinking, and develop theoretical concepts and tools,
   4. Understand relevant research methodologies and techniques and their appropriate application within his/her research field,
   5. Analyze critically and evaluate his/her findings and those of others,
   6. Question and find out innovative approaches.
   7. Acquire scientific knowledge and work independently,
   8. Effectively express his/her research ideas and findings both orally and in writing
   9. Be aware of issues relating to the rights of other researchers and of research subjects e.g. confidentiality, attribution, copyright, ethics, malpractice, ownership of data

   Method of assessment

   1. Written exam
   2. Homework assignment
3. To reduce Euler-Lagrange equations on the tangent bundle of a Lie group under symmetries

   Contribution to Program Outcomes

   1. Define and manipulate advanced concepts of Mathematics in a specialized way
   2. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
   3. Gain original, independent and critical thinking, and develop theoretical concepts and tools,
   4. Understand relevant research methodologies and techniques and their appropriate application within his/her research field,
   5. Analyze critically and evaluate his/her findings and those of others,
   6. Question and find out innovative approaches.
   7. Acquire scientific knowledge and work independently,
   8. Develop mathematical, communicative, problem-solving, brainstorming skills.
   9. Effectively express his/her research ideas and findings both orally and in writing
   10. Be aware of issues relating to the rights of other researchers and of research subjects e.g. confidentiality, attribution, copyright, ethics, malpractice, ownership of data

   Method of assessment

   1. Written exam
   2. Homework assignment

Contents
Week 1:	Introduction to basic concepts, and the motivation
Week 2:	Hamiltonian systems on symplectic manifolds,
Week 3:	Canonical Hamiltonian systems on the cotangent bundles
Week 4:	Lagrangian mechanics
Week 5:	Variational Principles and Constraints
Week 6:	Introduction to Lie groups
Week 7:	Introduction to Lie algebras
Week 8:	Poisson bracket. Midterm Exam.
Week 9:	Poisson manifolds
Week 10:	Momentum maps
Week 11:	Computation and properties of momentum maps
Week 12:	Lie-Poisson reduction
Week 13:	Euler-Poincaré reduction
Week 14:	Coadjoint Orbits
Week 15*:	-
Week 16*:	Final Exam
Textbooks and materials:	Marsden, J.E. and Ratiu, T.S. [1994], Introduction to Mechanics and Symmetry. Volume 75 of Texts in Applied Mathematics, second printing of second edition
Recommended readings:	Abraham, R. and Marsden, J.E. [1978], Foundations of Mechanics. Addison-Wesley, second edition. Marsden, J.E. and Ratiu, T.S. [1994], Introduction to Mechanics and Symmetry. Volume 75 of Texts in Applied Mathematics, second printing of second edition Holm, D. D., Schmah, T., & Stoica, C. (2009). Geometric mechanics and symmetry: from finite to infinite dimensions (Vol. 12). Oxford University Press. 2003. Springer-Verlag. Libermann, P., & Marle, C. M. (2012). Symplectic geometry and analytical mechanics (Vol. 35). Springer Science & Business Media. Arnold V.I.(1989). Mathematical Methods of Classical Mechanics. 2nd ed., Springer.
	* Between 15th and 16th weeks is there a free week for students to prepare for final exam.

Assessment
Method of assessment	Week number	Weight (%)
Mid-terms:	8	40
Other in-term studies:		0
Project:		0
Homework:	4,12	10
Quiz:		0
Final exam:	16	50
	Total weight:	(%)

Workload
Activity	Duration (Hours per week)	Total number of weeks	Total hours in term
Courses (Face-to-face teaching):	3	14
Own studies outside class:	6	14
Practice, Recitation:	0	0
Homework:	10	2
Term project:	0	0
Term project presentation:	0	0
Quiz:	0	0
Own study for mid-term exam:	15	1
Mid-term:	3	1
Personal studies for final exam:	20	1
Final exam:	3	1
		Total workload:
		Total ECTS credits:	*
	* ECTS credit is calculated by dividing total workload by 25. (1 ECTS = 25 work hours)