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Analytical Mechanics I (Fall 2014)
General:
This is a B.Sc. course, which will be held in Physics Department of Sharif University of Technology.
Class Time: Sunday and Tuesday 8:30 - 10:30
Place: Class Hall 3 - تالار ها - تالار 3
Registered students: 70
About the Course:
This is an introductionary 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)
Grading:
Final Exam : 7 points YOU CAN SEE THE RESULTS HERE.
Mid-term 2: 5 points YOU CAN SEE THE RESULTS HERE.
Mid-term 1: 4 points YOU CAN SEE THE RESULTS HERE.
9 November 2014 - @ 8:30 - Class Hall No. 3 / امتحان میان ترم 1 - 18 آبان 93 ساعت 8:30 مکان تالار 3
Assignments: 4 points
Essay and Presentation: bonus points
Quiz: bonus points
Total grade: 20 + bonus points YOU CAN SEE THE TOTAL GRADING HERE
TA Classes:
This course will have a three TA classes
1) Group 1 : Miss Fatemeh Bagheri
2) Group 2 : Mr. Abbas Alizadeh
3)Group 3: Mr. Amin Safdari
Suggested Reading:
will be updated...
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:
will be updated...
Time Line of Lectures:
Lecture 1: (30/06/93)
First there will be a brief explanation about the course. A couple of minutes on physics History. In this lecture we also introduce the concept of the classical mechanics. The predictability and reversibility of physical laws. Then we introduce the mathematical inquiries for studying the analytical mechanics. (Chapter I)
Lecture 2: (01/07/93)
In this lecture, we review the concept of classical mechanics. The concept of system, degree of freedom and phase space is re-studied. Then we go for the vector analysis. The concept of coordinate change. Rotation, degree of freedom is discussed. We show that the Rotation has a 3 degree of freedom in 3-dimension. (Chapter I)
Lecture 3: (06/07/93)
In this lecture we start talking about the scalars, vectors and tensor ad also the concept of the group theory. We discuss about the rotation transformation (Chapter I)
Lecture 4: (08/07/93)
In this lecture, we study the spherical coordinates. We obtained the velocity and acceleration in polar and spherical coordinates. We introduce the concept of derivatives and the gradient. (Chapter I)
13 /07 / 93 - public holiday
Lecture 5 : (15/07/93)
The basics of Newtonian Mechanics, the concept of inertial frames, relativity of Galileo and the problem of accelerated frame is discusses. The laws of Newton is discussed as well. (Chapter II)
Lecture 6 : (20/07/93)
In this lecture we study a couple of problems in dynamics, emphasizing on the concept of force, frictional force and problem solving techniques. (Chapter II)
Lecture 7 : (22/07/93)
In this lecture, we study the concept of Energy, potential energy and conservation of Energy-momentum and angular momentum, we also discuss the limitations of Newtonian Mechanics. (Chapter II)
Lecture 8 : ( 27/07/93)
In this lecture, we study the harmonic oscillator problem and we start solving couple of problems in this framework. ( Chapter III)
Lecture 9 : (29/07/93)
In this lecture, we continue with study the harmonic oscillator chapter and we discuss different aspect of mechanical physics problem solving methods ( Chapter III)
Lecture 10 : (04/08/93)
In this lecture, we study the concept of Fourier series and Fourier transformation and we discuss its application in solving mechanical systems with the assumption of superposition.
In this lecture, we continue with the concept of Fourier transformation. Then we introduce the concept of Green function as method to solve forced-damped harmonic oscillator problem. (Chapter III)
In this lecture, we start studying the Chapter 4- Chaos. The characteristics of non-linear differential equations is discussed. We also discuss the properties of phase space in chaotic problems. The sensitivity of the solution to the initial conditions is also presented. (Chapter IV)
13 /08 / 93 - public holiday
In this lecture, we will continue the phenomenology of chaotic problems. we will discuss about jumps, hysteresis and phase lags. We also we study the chaos in pendulum. (Chapter IV)
In the first part of the lecture we discuss the concept of turbalance in fluids. Reynolds numbers and the phase of chaos in fluids. In the second part of the lecture, we start with the Gravitation chapter and we introduce the concept of gravitational field and gravitational potential. (Chapter IV, V)
In this lecture we restudy the gravitationa potential concept. We introduce the Poisson equation and solev a couple of problems, then we talk about the dark matter problem. (Chapter V)
In this lecture we will talk about the tidal forces and we solve couple of problems in gravitational physics. (Chapter V)
In this lecture we will study the Lagrange equation with constraints. Then we will study the equivalence of Newtonian Physics and Lagrangian formalism and finally we will discuss the Conservation laws. (Chapter VII)
In this lecture we will restudy the concept of conservation and symmetry. Then we will start the Hamiltonian Dynamics. (Chapter VII)
30 /09 / 93 - public holiday
02 /10 / 93 - public holiday
Assignments:
1) Problem Set 1 due to Sunday 19 October - 27 مهر
2) Problem Set 2 due to Sunday 2 November- 11 آبان Solutions: Q2-4-6 / Q3a , Q3b, / Q5a, Q5b
3) Problem Set 3 due to Sunday 9 November- 18 آبان
4) Problem Set 4 due to Sunday 7 December - 16 آذر
5) Problem Set 5 due to Sunday 14 December - 23 آذر
6) Problem Set 6 due to Tuesday 16 December - 25 آذر
7) Problem Set 7 due to Sunday 4 January 2015 - دی 14
8) Problem Set 8 due to Tuesday 20 January - دی 30
9) Problem Set 9 due to Tuesday 20 January - دی 30
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: 90101019
6) Action - Angle Variables
7)Chaos Problems: Each Example of Chapter 4 of Marion: / 92100291 /
8)Phonos in Solid state physics as a classical mechanic problem: /92110551/
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
