HOW TO SELF LEARN CLASSICAL MECHANICS

 

Classical mechanics is one of the core subjects which is essential to learn advanced physics. This comprises of Lagrangian and Hamiltonian formulation, canonical transformation, Hamilton-Jacobi theory, and some elementary topics of chaos to start with. Once you are familiar with the theory you can jump into several applications of these topics in different fields of mechanics. Central forces, rotational mechanics, oscillations to name a few and you will encounter these topics in every other field of physics. You will be able to appreciate how beautifully the subject deals with mechanics from an entirely rigorous mathematical perspective. So, the subject has a good mixture of mathematics like every other physics subject and some brain-tricking intuitive thinking. Though there are many resources available online people get confused about where to start the topic and what are materials to follow.

So, let me start with the major pre-requisite for the subject: 

•   Strong Foundation of Newtonian Mechanics: This will help to understand the physical picture embedded in the mathematical formulation. You will appreciate the subject better and will understand why these formulations are superior to Newtonian mechanics.

• Mathematical Knowledge: Well most of us get confused at this part! “How much maths should I know to begin with? Will I end up as a mathematician rather than learning physics?” The short answer is once you are acquainted with threshold math you can start, but you need to spend quality time whenever you face new mathematical topics. Let me list some of the essential mathematical concepts you need to know:  
•  Calculus: You should have a thorough knowledge of concepts like partial differentiation, Lagrange multipliers in addition to integral and differential calculus. Solving some problems will help to hone your skills which is important.
•  Linear Algebra: You need to know some basic topics like eigenvalue and eigenvectors, matrix algebra, solving systems of equations. 
•    Calculus of Variation: A good hand on COV will be helpful, but knowing basic ideas will also do the job for you. You will understand all these concepts better once you find how COV is crucial in our new formulations.
• Legendre Transformation: You will encounter this concept at a later stage. But don’t worry! Most of the books cover essentials in a well-structured manner. You can dive into the mathematical part if you are interested and have ample time

I will list some of the books which will be very helpful for prerequisites:

1.      Calculus by Thomas or Steward Calculus: Both are fantastic books!

2.      Any standard Mathematical Physics book for advanced mathematical concepts

3.      Classical Mechanics by David Morin||Classical Mechanics by Marion and Thronton|| Concept of Physics by H.C Verma (obviously! :-) )|| B.M Sharma(For JEE level problems)|| Classical Mechanics by Kleppner and Kolenkov|| Fundamentals of Physics by Halliday Resnick and many more!! 

As a bottom line, I like to tell you that any shortcomings should not stop you from learning the subject, you can cross over any obstacles.

Now let’s get into the main business.  I will list some of the useful resources available and which are widely popular. Please mention in the comment box if you found something useful other than these materials.

Video Resources:

1.   NPTEL Videos by Prof. V.Balakrishnan:  These are some of the classic videos you can get on the internet. Absolute Gold!! Though topics are quite complicated he explains the topic in depth by considering its minute details in all aspects.

2.   NPTEL Videos by Prof. Charudatta Kadolkar:  This a standard 12-week NPTEL course. It covers all fundamental topics of advanced level. Prof.C.Kadolkar explains topics beautifully.

3.  Classical Mechanics Lectures by Prof. Joseph Linder: The good thing about the video is professor follows most of the topics from the Goldstein textbook in the same order. and you can watch these videos whenever you can't understand a particular topic.  The lectures aren't that rigorous so you are free to watch the required topic's video whenever you need. The video quality is quite bad is one con for this lecture series.

Prescribed Textbook:

1.   Classical Mechanics by Goldstein: This is one of the standard books used across the world at the master’s level. For absolute beginners, it might be difficult to follow or may take multiple readings, but it is worth giving try. The problems are really exciting and very helpful to understand the subject.

2.   Course of Theoretical Physics by Landau- Lishfitz: One of the Russian old school books from the great physicist Landau and Lifshitz. Conceptually very clear but it will take a lot of time for those who are seeing it for the first time. 

3.    Classical Mechanics by Greiner: This is another general book that is very useful for classical mechanics. It has some dedicated chapters for advanced classical mechanics which is very helpful

4.    Classical Mechanics by Corben: The specialty of this book is it teaches subject beyond math and there are some intuitive explanations which are very helpful in a rigorous mathematical-oriented subject.  You will understand what’s happening in the background of complicated Greek letters!

    There are many other good books on this subject. Since classical mechanics is one of the oldest topics in physics you will never run short of resources even if you decide to learn this subject for your lifetime. Mathematical Methods in Classical Mechanics by Arnold is the book which you should read if you are pro at understanding subject in a mathematically rigorous manner. You can refer to the Schaum series for tons of problems.     

Finally to begin with you can start with any of the lecture videos which is comfortable to you. I personally recommend starting with Prof.Charudatta Kadolkar's lectures and follow Goldstein. Once you are confident you can refer to other books.    Happy Learning!!!