Classical Mechanics I

The course is part of a set of courses devoted to Classical Mechanics, which is a branch of physics that studies the movement of masses and particles that includes the theory initiated by Galileo and Newton and developed in the XVIII and XIX century by Lagrange and Hamilton.

The contents of this broad field are distributed in the two basic courses Classical Mechanics I and II in the 2nd year, and in Classical Mechanics III, in the compulsory 3rd year. General objectives of Classical Mechanics I include the following:

- Introduce the basic concepts of Newtonian and Lagrangian formulations of mechanics and special relativity, for describing mechanical systems and wave phenomena.

- Describe the most relevant applications understanding how the fundamental principles are involved in solving the equations of motion.

- To familiarize the student with appropriate mathematical techniques to solve problems and provide the ability to manipulate concepts to solve these problems creatively.

- To familiarize the student with the terminology and notations of modern physics that will facilitate the transition to the study of other areas of physics, especially quantum mechanics.

As a result of learning, the student:

- Will understand the key concepts of Newtonian mechanics and will be able to solve problems of dynamics particles and systems dynamics integrating the equations of motion and using the conservation laws.

- Will understand the effects that occur when the reference system is not inertial and will be able to calculate those effects.

- Use the Lagrangian method to obtain the system equations of motion and understand the relationship between symmetries and conservation laws.

- Will work with linear oscillator systems knowing how to apply the mathematical methods that allow to obtaine the solutions.

- Will solve the wave equation in one dimension, will distinguish the concepts of phase and group velocity in a dispersive media, and will be able to perform Fourier analysis of a given wave.

1. NEWTONIAN MECHANICS
- Newton's Laws. Inertial Systems. Galilean transformations
- Conservation Theorems
- Examples of integration of the Newton equations.
- Harmonic oscillator. Damped and forced oscillations. Resonance.
- Non-inertial systems: centrifugal and Coriolis forces. Foucault's Pendulum.

2. LAGRANGE EQUATIONS
- Constrains and generalized coordinates.
- Principle of d'Alembert and Lagrange equations.
- Symmetry and conservation laws.

3. LINEAR OSCILLATIONS
- Theory of coupled oscillators. Normal modes.
- The continuous string as the limit of discrete set of oscillators. Wave equation.

4. WAVES
- General solution of the wave equation in one dimension.
- Wave packets, phase and group velocities. Dispersion.
- Fourier representation.
- Plane, spherical and cylindrical waves.

BASIC
- J. B. Marion: Dinámica clásica de las partículas y los sistemas. Ed. Reverté, 2000. (3-A03-9)
- H. Goldstein: Mecánica clásica. Ed. Reverté, 2000. (3-A03-8)
- John R. Taylor: Classical mechanics, University Science Books, 2004 (3-A03-248).
Mecánica Clásica, Editorial Reverté, 2013 (español)

OTHER TEXTBOOKS
- K. R. Symon: Mecánica. Ed. Aguilar, 1970. (3-A03-44)
Mechanics. Addison-Wesley, 1971. (3-A03-107)
- A. P. French: Mecánica Newtoniana, Reverté 1978. (3-A03-40)
Vibraciones y ondas. Reverté 1991. (3-A03-41)
- F.S. Crawford: Ondas. Berkeley Physics Course v. 3. Ed. Reverté, 1979. (A03-125)
- Tai L. Chow: Classical mechanics, John Wiley, 1995 (3-A03-144).
- Atam P. Arya: Introduction to Classical Mechanics, Prentice Hall, 1998 (3-A03-166)

SOLVED PROBLEM BOOKS
- O. Ecenarro. Problemas de mecánica resueltos y comentados. Universidad del Pais Vasco, 2000. (3-A03-190)
- O. Ecenarro. Mecánica y Ondas: Problemas de examen resueltos y comentados. Universidad del Pais Vasco, 2000. (3-A03-216)
- V.M. Pérez García, L. Vázquez Martínez y A. Fernández-Rañada: 100 problemas de mecánica, Alianza editorial, 1997. (3-A03-159)
- David Morin: Introduction to Classical Mechanics. With Problems and Solutions, Cambridge University Press, 2008. (3-A03-269)

Internet resources:
Virtual classroom: it will include teaching material done by the professors, links to free books without copyright and online resources.

Electronic books:
https://prelo.usc.es/

The basic and general competences are given in the Memory of the Degree in Physics of the USC, where they can be consulted. The transversal competences are: the acquisition of capacity for analysis and synthesis, organisational and planning capacity, and critical reasoning development.

The specific competences are:

- Acquire a good understanding of the most important physics theories, identifying in their logical and mathematical structures, their experimental basis as well as the physical phenomena described by them.

- Be able to handle orders of magnitude and make adequate estimates with a clear perception of situations that, although physically different, show some analogy, allowing the use of solutions known in new problems.

- Be able to identify the essential in a physical process by establishing a work model of the same, as well as performing the necessary approaches to reduce the problem to a manageable level.

- Understand and master the use of mathematical and numerical methods most commonly used in physics.

- Be able to handle, search and use bibliography, as well as any relevant source of information to apply it in research and development projects.

The course takes place in the first semester with 4 teaching hours per week (2 hours are expositive and 2 hours are of interactive type).

The expositive lectures will deal with theory. The student will know in advance the content of the lesson and the bibliography. The interactive lectures will be given in small groups and they seek a greater student participation. Interactive classes may consist of blackboard presentations of exercises and problems either by the teacher or by the students.

Tutorial lectures can be in-person or telematic. In both cases an appointment with the professor is needed.

The course will have a Moodle Virtual Classroom, which will include additional materials such as lectures notes, problem sets, links to websites of interest, links to online resources and web pages, and any other information relevant to the course.

The general evaluation criteria specified in the memory of "Grado" will be applied.

At the end of each lesson a control exam will be made during the interactive lectures that will consist in the resolution of a problem. Continuous assessment will take into account the outcome of these tests, together with the assistance and active participation of students in classes and completion of the tasks proposed. This part of the grade will account for 40% of the final grade.

There will be a final exam that will weigh 60% in the final grade. In any case, to pass the course it will be a necessary condition that the mark in the final exam is not smaller than 3.5.

The grade obtained by the student will not be less than the one obtained in the final exam.

In case of fraud in the realisation of exams or tests what is written in the “Normativa de avaliación do rendemento académico dos estudantes e de revisión de cualificacións” will be enforced.

Blackboard Lectures in Large Groups: 32 hours
Blackboard Lectures in small Group: 24 hours
Individual Tutoring: 4 hours

Individual study outside the classroom: 75 hours
Writing exercises and other works: 15 hours

It is recommended to have completed General Physics I and II and Mathematical Methods I, II, III and IV. The course is complemented by the laboratory of mechanics in Experimental Techniques II.

Regarding the study of the subject, it is recommended to attend and participate actively in class, keep up the study of the contents taught using the proposed bibliography, solve the proposed problems individually or in groups and take advantage of tutorials to solve doubts.