Lectures: MW, 8:45-10:00 a.m., in HCB 212.
Lectures: MW, 8:45-10:00 a.m., in HCB 212.
Lecturer: Prof. Laura Reina, 510 Keen Building,
644-9282, e-mail: click
here
Office Hours: Tuesday, from 12:30-2:30 p.m.
The most efficient way to contact me outside office hours is
by e-mail. If you need to see me in person, you should make an
appointment.
Text:
L. D. Landau and E. M. Lifshitz, Mechanics
Butterworth-Heinemann Publisher (Third Edition). [LL]
H. Goldstein, C. Poole, and J. Safko, Classical Mechanics ,
Addison Wesley (Third Edition). [Gol]
Topics and Objectives
Classical mechanics studies the motion of material bodies. It is among
the fundamental branches of modern physics and is therefore an
essential component of all graduate programs in Physics. This course
introduces the structure of classical mechanics and discusses some of
its most important applications in modern physics.
In the first part of this course, we will start from the Lagrangian
formulation of classical mechanics and study the solution of the
equations of motion of several systems, from simple one-body systems,
to more complex systems acted upon by central forces and rigid bodies,
up to scattering problems and oscillations. We will also extend our
discussion to include the theory of special relativity.
The second part of this course will introduce the hamiltonian
formulation of classical mechanics and study its formal and physical
consequences. More advanced topics, such as non-linear dynamics and
continuous systems, will be discussed in the third part of this
course, depending on time availability.
Here is a summary of the topics covered in class lecture by lecture:
| Date | Topics covered | Main reference | 08/24 | Syllabus. Review of Newtonian mechanics for a single particle and a system of particles. | Your notes. [Gol] (Ch. 1, Sec. 1.1-1.2) | 08/26 | Introduction to Lagrangian mechanics: Lagrangian equations of motion from d'Alembert principle. | [Gol] (Ch. 1, Sec. 1.3-1.5) | 08/31 | Applications of Lagrangian approach: simple examples. | [LL] (Ch. 1, Sec. 6 and Problems), [Gol] (Ch. 1, Sec. 1.6) | 09/02 | Derivation of Lagrange's equations from a variational principle (Hamilton's principle). | [LL] (Ch. 1, Sec. 1-2), [Gol] (Ch. 2, Sec. 2.3) | 09/09 | Noether's theorem. Conservation of linear and angular momentum, conservation of energy. Examples. | [LL] (Ch. 2), [Gol] (Ch. 2, Sec. 2.6-2.7), your notes | 09/14 | Hamilton's principle for non-holonomic systems, introduction of Lagrange multipliers. Examples. | [Gol] (Ch. 2, Sec. 2.4), your notes. | 09/16 | Lagrange multipliers: examples (continued). Introduction to the problem of central-force motion. | [Gol] (Ch. 2, Sec. 2.4, 3.1), your notes. | 09/21 | Central force problem: reduced system, Lagrangian, equations of motion. Central force problem: first integrals, integration of motion. | [LL] (Ch. 3, Secs. 13-14), [Gol] (Ch.3, Secs. 3.1-3.2) | 09/23 | Central force motion: classification of the orbits from the study of the equivalent one-dimensional problem. The differential equation for the orbit. | [LL] (Ch. 3, Secs. 11-14), [Gol] (Ch. 3, Secs. 3.3 and 3.5) | 09/28 | FIRST MIDTERM EXAM | 09/30 | The Kepler problem. Solution of the orbit equation/integration of the motion from its first integrals. Form and properties of the orbits. | [LL] (Ch. 3, Sec. 15), [Gol] (Ch. 3, Sec. 3.7) | 10/05 | Derivation of Kepler's laws. The motion in time in the Kepler problem. | [LL] (Ch. 3, Sec. 15), [Gol] (Ch. 3, Secs. 3.7-3.8) | 10/07 | Scattering in a central force field, i.e. the problem of open orbits. Rutherford scattering. | [LL] (Ch. 3, Sec. 18), [Gol] (Ch. 3, Sec. 3.10) | 10/12 | Scattering problem: trasformation to laboratory coordinates. | [LL] (Ch. 3, Sec. 17), [Gol] (Ch. 3, Sec. 3.101) | 10/14 | Oscillations: example of two coupled harmonic oscillators. Discussion of homework problems. | [LL] (Secs. 21 and 23), [Gol] (Ch. 6, Secs. 6.2 and 6.4 ) | 10/19 | Oscillations: formalism of small oscillations and the eigenvalue problem. | [LL] (Secs. 23-24), [Gol] (Ch. 6, Secs. 6.1-6.2) | 10/21 | Rigid body motion: degrees of freedom, generalized coordinates; space frame vs body frame; linear and angular momentum, kinetic energy; inertia tensor. | [LL] (Secs. 31-32), [Gol] (Ch. 4, Secs. 4.1 and 4.9. Ch. 5, Sec. 5.1) | 10/26 | Rigid body motion: principal moments of inertia. Some examples. Steiner's theorem. | [LL] (Sec. 32), [Gol] (Ch. 5, Secs. 5.3-5.4) | 10/28 | Rigid body motion: Euler angles. Euler's equations of motion. | [LL] (Secs. 35-36), [Gol] (Ch. 4, Secs. 4.4 and 4.6. Ch. 5, Sec. 5.5.) | 11/02 | SECOND MIDTERM EXAM | 11/04 | NO CLASS, NO HOMEWORK DUE | 11/09 | Rigid body motion: motion of a torque-free rigid body. | [LL] (Secs. 35-36), [Goldstein] (Ch. 5, Sec. 5.6) | 11/13 | MAKE-UP CLASS, HCB 212, 9:05-10:20 a.m. | 11/16 | Hamilton's equations of motion. Hamiltonian function and its properties. | [LL] (Secs. 40-42), [Gol] (Ch. 8, Secs. 8.1-8.2 and 8.5) | 11/18 | Canonical transformations: introduction and general properties. | [LL] (Sec. 45), [Gol] (Ch. 9, Secs. 9.1-9.3) | 11/23 | Canonical transformations: more properties and examples. | {LL] (Sec. 45), [Gol] (Ch. 9, Secs. 9.1-9.3) | 11/30 | Canonical transformations: simplectic approach to hamilton dynamics. | [Gol] (Ch. 9, Secs. 9.4-9.5) | 12/02 | Liouville's Theorem. | [LL] (Sec. 46), [Gol] (Ch. 9, Sec 9.9) | 12/10 | FINAL EXAM |
|---|
Course format and student responsibilities
The textbook will be followed pretty closely, but new material will be
introduced to complement and broaden the discussion of several
topics. It is the students' responsibility to attend class and take
notes of the material that is not in the textbook.
A graduate level course in classical mechanics has a quite formal
approach to all topics discussed. However, physics is learned by
doing, in particular by solving problems in order to consolidate the
theory. Part of class time will be devoted to problem solving and more
problems will be assigned in the homework. It is the students'
responsibility to solve them carefully and use them to attain a
maximum degree of practice with the subject matter.
Homework
The homework will be assigned on a weekly basis, on Wednesday, due the next Wednesday at class time. It will consist of graded and non-graded problems. Only the graded problems will have to be returned by the due date. Solutions will be posted (for all problems, both graded and non-graded) on the course web page. I will not accept late homework except for special circumstances (to be discussed with me ahead of time). There will be no make-up for late or missed homework.
Exams and Grades.
A student's grade will be based 30% on the homework, 40% on two Midterm Exams (20% each) and 30% on the Final Exam. Letter grades will be determined from numerical grades as follows:
100-85% : A
84-70% : B
69-55% : C
54-40% : D
below 40% : F
Attendance, participation, and personal interest will also be important factors in determining a student's final grade, and will be used to the discretion of the instructor.
The Midterm exams are tentatively scheduled for Monday September, 28th 2015 ( exam and solutions ) and Monday November, 2nd 2015 ( exam and solutions ). A change of dates will be announced in class and on the course web page with advanced notice. The exams will be given in class, and they will last for the entire class time.
The Final exam will be on Thursday December, 10th 2015 from 3:00 till 5:00 p.m. The Final exam will consist of three sections: 1) make-up section for Midterm 1, 2) make-up section for Midterm 2, 3) Final exam section. Section 1) and 2) are thought for people who need to improve the grade of the Midterm Exams. People who do not have to improve those grades should skip these sections. Section 3) is for everybody and covers the topics discussed in class after Midterm 2. The grade of the Final Exam will be based on Section 3) only.
Exam Policy
An absence may be excused given sufficient evidence of extenuating circumstances and in accordance with the University policy stated below. In such a case, extra weight will be attached to the other exams. Barring emergencies, the matters leading to a possible excused absence should be discussed with the instructor well in advance. An unexcused absence will result in a grade of zero.
Attendance and Absence
Regular, responsive, and active attendance is highly recommended. A student absent from class bears the full responsibility for all subject matter and information discussed in class. Please inform me in advance of any excused absence (e.g., religious holiday) on the day an assignment is due. In case of unexpected absences, due to illness or other serious problems, we will discuss the modality with which you will turn in any missed assignment on a case by case basis. Other situations are discussed under ``University Attendance Policy'' below.
University Attendance Policy
Excused absences include documented illness, deaths in the family and other documented crises, call to active military duty or jury duty, religious holidays, and official University activities. These absences will be accommodated in a way that does not arbitrarily penalize students who have a valid excuse. Consideration will also be given to students whose dependent children experience serious illness.
Academic Honor Policy
The Florida State University Academic Honor Policy outlines the University’s expectations for the integrity of students’ academic work, the procedures for resolving alleged violations of those expectations, and the rights and responsibilities of students and faculty members throughout the process. Students are responsible for reading the Academic Honor Policy and for living up to their pledge to “... be honest and truthful and ... [to] strive for personal and institutional integrity at Florida State University.” (Florida State University Academic Honor Policy, found at http://dof.fsu.edu/honorpolicy.htm) The policy is based on the premise that each student has the responsibility 1) to uphold the highest standards of academic integrity in the student's own work, 2) to refuse to tolerate violations of academic integrity in the University community, and 3) to foster a high sense of integrity and social responsibility on the part of the University community.
Americans with Disabilities Act
Students with disabilities needing academic accommodation should: (1) register with and provide documentation to the Student Disability Resource Center; and (2) bring a letter to the instructor indicating the need for accommodation and what type. This should be done during the first week of class. This syllabus and other class materials are available in alternative format upon request. For more information about services available to FSU students with disabilities, contact the:
Student Disability Resource Center
874 Traditions Way
108 Student Services Building
Florida State University
Tallahassee, FL 32306-4167
(850) 644-9566 (voice)
(850) 644-8504 (TDD)
sdrc@admin.fsu.edu
http://www.disabilitycenter.fsu.edu
Syllabus Change Policy
Except for changes that substantially affect implementation of the evaluation (grading) statement, this syllabus is a guide for the course and is subject to change with advance notice.