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**Analytical Mechanics I (Fall 2019)
**

General: (The webpage of the course is updated gradually) - Last Update 5 Febraury 2020

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: Lecture Hall (Talar) 6

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

Registered students: 84

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

Mohammad Hosein Sharifi email address: smhsksharifi@gmail.com

TA Class Group 1: TBA

TA Class Group 2: TBA

Grading:

Mid-term 1: 4 points
YOU CAN SEE THE RESULTS HERE.
** 13 Aban 1398 / 4 November 2019** @ 8:30 *

Mid-term 2: 5 points
YOU CAN SEE THE RESULTS HERE
**
25 Azar 1398 / 16 December 2019 @ 8:30** *

Assignments: 4 points YOU CAN SEE THE RESULTS HERE.

Final Exam : 7 points YOU CAN SEE THE RESULTS HERE. 25 Day 1398 / 15 January 20120 @ 9:00 - 12:00

Essay, Presentation and Class Activity: bonus points
(up to 1 point)
**16 Azar registration deadline / 16 Day Presentation Day**

Total grade: 20 + 1 YOU CAN SEE THE TOTAL GRADING HERE

*NOTE unusual time of exam

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

9) Analytical Mechanics for Relativity and Quantum Mechanics by Oliver Davis Johns (2005)

10) Classical Mechanics: Systems of Particles and Hamiltonian Dynamics by Walter Greiner (2001)

11) Analytical mechanics by A. Fasano (2006)

12) Analytical Mechanics by Nivaldo A. Lemos (2018)

13) Classical Dynamics: A Contemporary Approach by Eugene J. Saletan and Jorge V. José (1988)

14) Introduction to Classical Mechanics by Atam Parkash Arya (1990)

15) Analytical mechanics by Louis N. Hand, Janet D. Finch (1998)

Lectrure Notes and Presentations:

1- Lecture Note I: Classical Physics

Time Line of Lectures:

**Lecture
1: ( Saturday - 30 Shahrivar 1398 - 21 September 2019)**

This is the first lecture of the course. The structure of course is discussed. Then we start from definiation of classical physics with emphasising the concept of reversibility and predictibility in past and future.

**
Lecture 2: ( Monday - 1 Mehr 1398 - 23 September 2019 )**

In this lecture we finalize our study on the concept of classical physics. Then we investigate the coordinate transformation physics, between two inertial frames, we discuss the translation in time and space, rotation and boost. In this lecture the story of Pierre-Simon Laplace is told.

**
Lecture 3: ( Saturday - 6 Mehr 1398- 28 September 2019 )**

In this lecture we study about the basics of vector calculus.

**
Lecture 4: ( Monday - 8 Mehr 1398- 30 September 2019 )**

In this lecture, we study the concept of invariants and metric. In this lecture the story of Bernhard Riemann is told.

**
Lecture 5: ( Saturday - 13 Mehr 1398- 5 October 2019)**

In this lecture, we discuss the concept of derivative operator... Gradiant, divergence and curl.

**
Lecture 6: ( Monday - 15 Mehr 1398- 7 October 2019 )**

In this lecture we study the Newton's laws of motion. We discuss about their status (definition or law).

**Lecture 7 : (
Saturday - 20 Mehr 1398- 12 October 2019)**

In this lecture we discuss the concept of absolute space, by going through the ideas of Newton and Mach on rotating bucket. We also solve a problem about moving charged particle in constant magnetic field.

**
Lecture 8: ( Monday - 22 Mehr 1398- 14 October 2019 )**

In this lecture, we study the motion under resistive force and discuss that how the physicists make phenomenological models. In this direction we introduce the \chi square method. After that we go through the concept of equivalence principle.

**
Saturday - 27 Mehr 1398- 19 October 2019 : Official Holiday**

**Lecture 9: (
Monday - 29 Mehr 1398- 21 October 2019)**

In this lecture we discuss the concept of the conservation of the Energy, Angular momentum and linear momentum, then we discussed the limitations of classical mechanics.

**
Lecture 10: (
Saturday - 4 Aban 1398- 26 October 2019 )**

In this lecture we continue the limitations of classical physics and then we start the Chapter 3 - the oscillations.

**Lecture 11: (
Monday - 6 Aban 1398- 28 October 2019)**

In this lecture we continue our studies in Oscillatory motion. Specially we talked about the damped oscillations and phase diagram. In this lecture the story of Jim Peebles was told.

**
Lecture 12: (
Saturday - 11 Aban 1398- 2 November 2019 )**

In this lecture, we discuss the physics of damped harmonic oscillator with external force. The concept of resonance is discussed as well.

**Lecture 13: (
Monday - 13 Aban 1398- 4 November 2019)**

**Midterm Exam I - 13 Aban 1398 / 4 November 2019**

**
Lecture 14: (
Saturday - 18 Aban 1398- 9 November 2019 )**

In this lecture, we continue the chapter 3 with the solution of forced damped oscillations. We discuss the concept of Fourier transform. Correlation functions and power spectrum.

**
Lecture 15: (
Monday - 20 Aban 1398- 11 November 2019 )**

In this lecture, we continue the chapter 3 with the solution of forced damped oscillations. We discuss the concept of Green function. Then we discuss the RK4 as a numerical method to solve linear differential equations.

**
Lecture 16: (
Saturday - 25 Aban 1398- 16 November 2019 )
**

In this lecture we study the Gravity in the context of classical physics

**
Lecture 17: (
Monday - 27 Aban 1398- 18 November 2019 ) **

In this lecture, we continue our investigtion on the concept of gravity. We introduce the problem of dark matter as well.

**
Lecture 18: (
Saturday - 2 Azar 1398- 23 November 2019 )**

In this lecture we start the concept of variational method as a new venue for Hamiltonian formalism of mechanics.

**
Lecture 19: (
Monday - 4 Azar 1398- 25 November 2019 )**

In this lecture we continue with the study of the variational method. Specifically we show the second form of the Euler equation and we start the discussion on the idea of metrics.

**
Lecture 20: (
Saturday - 9 Azar 1398- 30 November 2019 )**

The lecture is cancelled due to air - poluution in Tehran - official holiday

**
Lecture 21: (
Monday - 11 Azar 1398- 2 December 2019 )**

Lagrangian Mechanics I

**
Lecture 22: (
Saturday - 16 Azar 1398- 7 December 2019 )**

Lagrangian Mechanics II

**Registration for Projects**

**
Lecture 23: (
Monday - 18 Azar 1398- 9 December 2019 )**

Lagrangian Mechanics III

**
Lecture 24: (
Saturday - 23 Azar 1398- 14 December 2019 )**

In this lecture we study the the concept of conjugate momentum, symmetries and conservation laws

**
Lecture 25: (
Monday - 25 Azar 1398- 16 December 2019 )**

Midterm Exam II-
**
25 Azar 1398- 16 December 2019 @ 8:30**

The EXAM is cancelled due to air - poluution in Tehran - official holiday

**
Lecture 26: (
Saturday - 30 Azar 1398- 21 December 2019 )**

In this lecture we study the Hamiltonian Mechanics, Poisson Brackets and Liouville theorem.

**
Lecture 27: (
Monday - 2 Day 1398- 23 December 2019 )**

Midterm Exam II-
**
2 Day 1398- 23 December 2019 @ 8:30**

**
Lecture 28: (
Saturday - 7 Day 1398- 28 December 2019 )**

Special Topics in Hamiltonian Mechanics I

**
Lecture 29: (
Monday - 9 Day 1398- 30 December 2019 )**

Special Topics in Hamiltonian Mechanics II

**
Lecture 30: (
Saturday - 14 Day 1398- 4 January 2020 )**

Chaos I

**
Lecture 31: ( Monday - 16 Day 1398- 6 January 2020 )**

**Chaos II -
Cancelled due to special Holiday Postponed to
Wednesday 18 Day 1398 - 8 January 2020**

Presentation day @ 8:30 - 10:30 (Postponed)

Assignments:

1) Problem Set 1 due to Saturday 4 Aban 1398 - 26 October 2019

2) Problem Set 2 due to Saturday 13 Aban 1398 - 4 November 2019

3) Problem Set 3 due to Monday 18 Azar 1398 - 9 December 2019

4) Problem Set 4 due to Monday 11 Azar 1398 - 2 December 2019

5) Problem Set 5 due to Monday 18 Azar 1398 - 9 December 2019

6) Problem Set 6 and Set 7 due to Final exam day

7) Problem Set 8 due to Final exam day (Possion Bracket Homework)

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.

**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 -**

9) The intersection of classical physicsm, statistical physics and quantum mechanics.

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