Classical Mechanics III

In a first part, it is intended that the student learns about some technical extensions of the topics that were studied in the previous courses Mecánica I and II. In a second part, a general treatment of continuous media will be presented.
Learning outcomes:

With respect to Classical Mechanics III, the student:

· Will be competent to solve mechanical problems through canonical formalism.
· Will know how to obtain approximate solutions to problems that are not solvable analytically.
· Will know how to analyze the stability of a system against disturbances.
· Will know the general formalism of continuous media description.
· Will be able to solve problems of continuous media.

Part A
1. Hamiltonian Mechanics
2. Dynamical Systems

Part B
3. Mechanics of Continuous Media
4. Fluid Mechanics

Basic bibliography:

PART A:

• Goldstein, H., Poole, C.e Safko, J., Classical Mechanics, third edition, Addison-Wesley, 2001.
• Gregory, R.D., Classical Mechanics, Cambridge University Press, 2006.
• Greiner, W., Classical Mechanics. Systems of Particles and Hamiltonian Dynamics, Springer, 2010.
• Scheck, F., Mechanics, Springer, 2010.
• Lemos, N.A., Analytical Mechanics, Cambridge University Press, 2018.
• Arnold, V.I., Mathematical Methods of Classical Mechanics, Springer-Verlag, 1989.
• Torok, J.S., Analytical Mechanics with Introduction to Dynamical Systems, Wiley & Sons, 2000.
• Upadhyaya, J.C., Classical Mechanics, Himalaya Publishing House, Second edition, 2014.
• Jose, J.V. y Saletan, E.J., Classical Dynamics: A contemporary approach, CUP, 1998.
• Simmons, F., Ecuaciones diferenciales, con aplicaciones y notas históricas, McGraw-Hill, 1972.

PART B:

• I.G. Currie, Fundamental mechanics of fluids, Mc. Graw-Hill, New York 1974,
• G. E. Mase, Mecánica del Medio Contínuo, Mc. Graw Hill, México, 1970
• G.E. Vekstein, Physics of Continuous Media. Adam Hilger.
• D.J. Acheson, Elementary Fluid Dynamics. Oxford.
• Frank M. White, Mecánica de Fluidos, McGrawHill, Madrid 2004,

Online resources:

• Aranda, P., Apuntes de Ecuaciones diferenciales I, Universidad Complutense de Madrid, 2009. http://jacobi.fis.ucm.es/pparanda/EDNpdf/apEDI9.pdf.
• Mas, J., Mecánica Teórica, Notes by Javier Mas, Departamento de Física de Partículas, USC, 2018. Available in the Virtual Classroom.
• Widget from WolframAlpha to draw phase maps: https://www.wolframalpha.com/widgets/view.jsp?id=9298fea31cf266903b3df7…
• Virtual Classroom: Notes made by the teachers, problem bulletins, problem solutions, exams from previous courses.
• Virtual Classroom: Links to online resources.

BASIC AND GENERAL:

CB1 - That the students demonstrated to possess and understand knowledge in a study area that is part of the general secondary education base, and is often found at a level that, although based on advanced textbooks, also includes some aspects that imply knowledge derived from the vanguard of its field of study.
CB2 - That students know how to apply their knowledge to their work or vocation in a professional way and possess the skills that are usually demonstrated through the elaboration and defense of arguments and the resolution of problems within their area of study.
CB3 - That students have the ability to gather and interpret relevant data (usually within their area of study) to issue judgments that include a reflection on relevant social, scientific or ethical issues.

CG1 - Possessing and understanding the most important concepts, methods and results of the different branches of Physics, with a historical perspective of its development.
CG2 - Have the ability to gather and interpret data, information and relevant results, obtain conclusions and issue reasoned reports on scientific, technological problems or other areas that require the use of knowledge of Physics.
CG3 - Apply both the theoretical and practical knowledge acquired as the capacity for analysis and abstraction in the definition and formulation of problems and in the search for their solutions in both academic and professional contexts.

TRANSVERSAL:

CT1 - Acquire capacity for analysis and synthesis.
CT2 - Have organizational and planning capacity.
CT5 - Develop critical thinking.

SPECIFIC:

CE1 - Have a good understanding of the most important physical theories, locating in their logical and mathematical structure, their experimental support and the physical phenomenon that can be described through them.
CE2 - Be able to clearly handle the orders of magnitude and make appropriate estimates in order to develop a clear perception of situations that, although physically different, show some analogy, allowing the use of known solutions to new problems.
CE5 - Be able to realize the essential of a process or situation and establish a model of work of the same, as well as to carry out the necessary approaches in order to reduce the problem to a manageable level. It will demonstrate critical thinking to build physical models. CE6 - Understand and master the use of mathematical and numerical methods most commonly used in Physics
CE8 - Be able to handle, search and use bibliography, as well as any relevant source of information and apply it to research work and technical development of projects

A course will be activated on the Moodle platform of the Virtual Campus, to which information of interest to the student and additional teaching material will be uploaded.

The general methodological indications established in the USC Degree Physics Report will be followed. Teaching will be face-to-face and is scheduled in theoretical classes (24 hours), small group practices (18 hours) and tutoring in very small groups (3 hours).

In the theoretical and practical classes the basic contents of the subject will be presented and some exercises will be solved.

The most advanced contents and problems will be proposed to the student for their personal work with the support of the tutoring hours.

The tutorials may be face-to-face or telematic, if they are telematic they will require an appointment, which will also be recommended for face-to-face.

The qualification of the students consists of two parts:

• A final face-to-face exam to be held on the official dates set by the center, with a NE score that weights 60% in the final score.
• The continuous evaluation EC, weighting 40% of the final score, that will consist of attendance and active participation in face-to-face classes and tutorials, as well as delivery of exercises, projects, etc.


The final grade (NF) will be obtained as the maximum between the final exam grade and the result of averaging the EC course grade with the grade obtained in the NE final exam using the formula NF = Max (NE, EC * 0.4 + NE * 0.6 ) as long as NE is bigger or equal to 3.5, otherwise NE will be used as the final grade. This system will be applied both in the first and in the second opportunity.

Continuous assessment will only be valid during the academic year, and will not be kept for subsequent years.

In cases of fraudulent performance of exercises or tests, the one set forth in the Regulations for the evaluation of the academic performance of students and the review of grades will be applied .

24 hours of face-to-face or telematic lectures.
18 hours of interactive classroom or telematic classes.
3 hours of face-to-face or telematic tutoring.

As a general indication, in the USC's Memory of the Degree in Physics, the student's personal work is estimated at 50 hours, not counting face-to-face or telematic teaching, and the writing of exercises, conclusions or other works in 17.5 hours. Total 67.5 hours.

Attendance and active participation in theoretical and practical classes. Taking advantage of tutoring. Previously advised subjects: Classical Mechanics I and II, Mathematical Methods I, II, III, IV and V.