Instructor: Alok Shukla
Office: Room # 221 (2nd floor), Physics Bldg.
Phone: X-7576
E-mail: shukla@phy.iitb.ac.in
Office Hours: Feel free to drop in anytime.

Course Outline

This course is all about an introduction to the techniques of modern classical mechanics. I will assume that you are familiar with Newton’s equations. Additionally, basic knowledge of partial derivatives, and related concepts such as gradient, divergence, curl, divergence theorem (Gauss’s theorem), and Stokes’ theorem will be assumed. Rest of the methodology will be developed as the course progresses. I plan to cover the following topics during the semester:

1. Review of Newton‘s laws of motion, work-energy theorem, conservative and non-conservative forces, and the concept of potential energy function.
2. Constraints, generalized coordinates, virtual displacements, principle of virtual work, D’Alembert’s principle, Lagrangian, and Lagrange equations.
3. Variational principles and Lagrange’s equations.
4. The central force problem. Derivation of Kepler’s laws for the gravitational problem.
5. Rotating frames of references, and pseudo forces.
6. The kinematics and dynamics of rigid-body motion. Moment of inertia tensor, principle axes, and Euler’s equations. Torque-free motion of a rigid body. Dynamics of a heavy symmetrical top with one fixed point.
7. Theory of small oscillations.
8. Legendre transformation and Hamilton’s equations of motion.
9. Canonical transformations and Poisson’s brackets.
10. Hamilton-Jacobi theory and action angle variables.

Suggested Books

We are fortunate that a large number of excellent textbooks have been written on this subject. Inexpensive Indian editions of most of these books are available.

Textbook

• Classical Mechanics (3rd edn), by H. Goldstein, C. Poole, and J. Safko , Pearson Education (2007).

Reference Books

1. An Introduction to Classical Mechanics (2nd edn), by D. Kleppner and R. Kolenkow, Cambridge University Press (2014). Indian reprint of the first edition is widely available, and is quite good.
2. Analytical Mechanics by L. N. Hand and J. D. Finch, Cambridge University Press (1998).

Attendance Requirements

IIT Bombay rules require that all students attend at least 80% of the lectures in each course. This is precisely what I also expect you to follow.

Examinations and Grading

Your final grade will be based upon your performance in the following:

1. Quizzes (2): 15 %+15 %
2. Midsem Exam: 30 %
3. Final Exam: 40 %

Tutorial Sheets and Notes

• Tutorial Sheet 1
• Tutorial Sheet 1: Solution
• Tutorial Sheet 2
• Tutorial Sheet 2: Solution
• Tutorial Sheet 3
• Tutorial Sheet 3: Solution
• Notes on Central Force Problem (without using the Lagrangian approach)
• Tutorial Sheet 4
• Tutorial Sheet 4: Solution
• Tutorial Sheet 5
• Tutorial Sheet 5: Solution
• Tutorial Sheet 6
• Tutorial Sheet 6: Solution
• Tutorial Sheet 7
• Tutorial Sheet 7: Solution
• Tutorial Sheet 8
• Tutorial Sheet 8: Solution