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**Analytical Mechanics I (Fall 2018)
**

General: (The webpage of the course is updated gradually) - Last Update 26 January 2019

This is a B.Sc. course, which will be held in Physics Department of Sharif University of Technology.

Class Time: Saturday and Monday 9:00 - 10:30

Place: Talar 4

Office Hours: Sunday
8:00 - 9:00 / Tuesdays 8:00 - 9:00
(Or by appointment - Email: baghram@sharif.edu) ** **

Registered students:

About the Course:

This is an introductory course on Analytical Mechanics, one of the main courses of Physics department for B.Sc. students.

The main course book is: Classical Dynamics of Particles and Systems by Stephen T. Thornton and Jerry B. Marion

Cengage Learning; 5 edition (July 7, 2003)

----------------------------------------------------------------------------------

**Teacher Assitants:**

Hamed Kameli email address: hkameli@gmail.com

Javad Tabatabaie email address: smjty25@gmail.com

TA Class Group 1: Mr. Kameli will be in the library of Physics department Tuesday's from 17:00 till 19:00

TA Class Group 2: TBA

Grading:

Mid-term 1: 4 points YOU CAN SEE THE RESULTS HERE. 14 Aban 1397 / 5 November 2018 @ 8:30 *

Mid-term 2: 5 points YOU CAN SEE THE RESULTS HERE 12 Azar 1397 / 3 December 2018 @ 8:30

Assignments: 4 points YOU CAN SEE THE RESULTS HERE.

Final Exam : 7 points YOU CAN SEE THE RESULTS HERE.

Essay and Presentation: bonus points

Total grade: 20 + bonus points YOU CAN SEE THE TOTAL GRADING HERE

*NOTE THE TIME CHANGE

Suggested Reading:

1) The theoretical Minimum by Leonard Susskind and George Hrabovsky - 2013

2) Classical Mechanics by John R. Taylor 2005

3)Classical Mechanics (3rd Edition) by Goldstein, Poole and Safko – June 25, 2001

4) Mechanics (3rd Edition) by Symon – January 11, 1971

5) Classical Mechanics (5th Edition) by Tom W B Kibble and Frank H Berkshire (Jun 3, 2004)

6) An Introduction to Mechanics by Daniel Kleppner and Robert Kolenkow (Nov 18, 2013)

7) Introduction to Classical Mechanics, David Morin, 2008

8) Mechanics- Landau and Lifshitz 1975

Lectrure Notes and Presentations:

Time Line of Lectures:

**Lecture
1: ( Saturday - 15 September 2018)**

Introduction to the course. The timeline of the lectures and sources. Discussion on Classical Mechanism, systems, laws, initial conditions and determinism.

**
Lecture 2: ( Monday - 17 September 2018 )**

In this lesson, we study the concept of coordinate transformation. The rotation is discussed in more detail and Galilean transformations are also under consideration. The life and time of Pierre-Simon Laplace (1749 - 1827) is discussed.

**
Lecture 3: ( Saturday - 22 September 2018 )**

In this lesson we go through the rotation transformation once again to emphasis the mathematical foundation behind it the orthogonality and degrees of a freedom are discussed.

**
Lecture 4: ( Monday - 24 September 2018 )**

In this lecture we define the derivative operators: gradient, divergence and curl. We solve couple of easy examples in this direction.

**
Lecture 5: ( Saturday - 29 September 2018)**

In this lecture we start discussing the three laws of Newton. We had an extensive discussion on the concept of definition/law of mass and force. The idea of inertial frame in the light of the first law of Newtonian mechanism is discussed.

**
Lecture 6: ( Monday - 1 October 2018 )**

In this lecture we continue our discussion on Newton's law. The concept of equivalence principle is discussed. Finally a specific example of the dynamic of charged particle in magnetic field is discussed.

**Lecture 7 : (
Saturday - 6 October 2018)**

In this lecture we study the concept of energy.

**
Lecture 8: ( Monday - 8 October 2018 )**

The Cocenpt of Energy, Potential energy and conserved force are studied.

**Lecture 9: (
Saturday - 13 October 2018)**

The Harmonic oscillator is discussed. we argue that why this type of potentials are useful in physical systems.

**
Lecture 10: ( Monday - 15 October 2018 )**

In this lecture we discuss the harmonic oscillator with the damped force. The phase space of this motion is discussed.

**Lecture 11: (
Saturday - 20 October 2018)**

In this lecture we solve a classical point of view of Rayleigh scattering.

**
Lecture 12: ( Monday - 22 October 2018 )**

The coupled oscillations is discussed.

**Lecture 13: (
Saturday - 27 October 2018)**

In this lecture we discuss the technique of Fourier transform to solve the periodic driven forces.

**
Lecture 14: ( Monday - 29 October 2018 )**

In this lecture we discuss the Green Theorem and show how we can apply this technique to solve the damped, force driven harmonic oscillator.

**
Lecture 15: ( Saturday - 3 November 2018 )**

An introduction to the Chaos.

**
Lecture 16: ( Monday - 5 November 2018 )
**

Midterm Exam - 7 Aban 1397 (Note the time change)

**
Lecture 17: ( Saturday - 10 November 2018 ) **

Discussion on Chaos.

**
Lecture 18: ( Monday - 12 November 2018 )**

Discussion on Chaos.

**
Lecture 19: ( Saturday - 17 November 2018 )**

Discussion on Chaos.

**
Lecture 20: ( Monday - 19 November 2018 )**

In this lecture we begin our journey on gravity.

**
Lecture 21: ( Saturday - 24 November 2018 )**

The tidal force is discussed in this lecture.

**
Lecture 22: ( Monday - 26 November 2018 )**

The last lecture on Gravity. We have a discussion on dark matter, baryonic Tully-Fisher relation and MOND.

**
Lecture 23: ( Saturday - 1 December 2018 )**

In this lecture we will start the variational method.

**
Lecture 24: ( Monday - 3 December 2018 )**

Midterm Exam - 12 Azar 1397

**
Lecture 25: ( Saturday - 8 December 2018 )**

Lagrangian Formalism I

**
Lecture 26: ( Monday - 10 December 2018 )**

Lagrangian Formalism II

**
Lecture 27: ( Saturday - 15 December 2018 )**

Lagrangian Formalism III

**
Lecture 28: ( Monday - 17 December 2018 )**

Hamiltonian Formalism I

**
Lecture 29: ( Saturday - 22 December 2018 )**

Hamiltonian Formalism II

**
Lecture 30: ( Monday - 24 December 2018 )**

Assignments:

1) Problem Set 1 due to Saturday 21 Mehr 1397 - 13 October 2018

2) Problem Set 2 due to Saturday 12 Aban 1397 - 3 November 2018

3) Problem Set 3 due to Saturday 21 Aban 1397 - 12 November 2018

4) Problem Set 4 due to Saturday 28 Aban 1397 - 19 November 2018

5) Problem Set 5 due to Saturday 12 Azar 1397 - 3 December 2018

6) Problem Set 6 due to Saturday Exam Day

7) Problem Set 7 due to Saturday Exam Day

Essays and Projects:

In the case you choose your project, please email and announce it. We can discuss about your projects via emails. You can ask TAs help also.

The projects can be done by 1 or 2 students. And for the last session of class there will be a 10 minute presentations.

**A very good example of an Essay
(click
here) : Essay on QFT by Mehdi Saravani Waterloo University**

**1) Numerical Solution Code to solve Oscillatory
problems with force and damping terms**

**2) The History of Classical Mechanics**

**3) Rayleigh scattering as a classical mechanic
problem.**

**4) The trajectory of a particle in
gravitational and magnetic fields of earth.**

**5) Two - Three and ... N body codes for
trajectory of particles in gravitational field**

**6) Action - Angle Variables**

**7)Chaos Problems: Each Example of Chapter 4 of
Marion**

**8)Phonos in Solid state physics as a classical
mechanic problem - **

**۹۵۱۰۹۱۸۹ - ۹۵۱۰۹۱۵۶**

Useful Links:

will be updated...

1) A lecture note on Classical Dynamics by Dr. David Tong - Cambridge and the home page of course.

2) Homepage of classical mechancs course by Philip 'Flip' Tanedo in University of California - Irvine

3) Online video lectures on Classical Mechanics by L. Susskind