Brief report on Science Academies Lecture Workshop on Classical Mechanics. Organized by Department of Physics, Loyola College, Chennai

Size: px

Start display at page:

Download "Brief report on Science Academies Lecture Workshop on Classical Mechanics. Organized by Department of Physics, Loyola College, Chennai"

Derek Allison
5 years ago
Views:

1 Brief report on Science Academies Lecture Workshop on Classical Mechanics (December 4-6, 2014) Organized by Department of Physics, Loyola College, Chennai Convener: Prof. V. Balakrishnan, Dept. of Physics, IIT Madras Coordinator: C. Joseph Prabagar, Dept. of Physics, Loyola College Lecturers: Profs. Arul Lakshminarayan, S. Lakshmi Bala, Suresh Govindarajan and V. Balakrishnan Dept. of Physics, IIT Madras, Chennai The Workshop began at 9.00 am on December 4, 2014 with a short inaugural function. Rev. Fr. Dr. G. Joseph Antonysamy (Principal, Loyola College) felicitated the gathering. Dr. P. Sagayaraj (Head, Dept. of Physics, Loyola College) and Dr. S. Pauline, Dept. of Physics, Loyola College welcomed the participants. Prof.V. Balakrishnan in his inaugural address briefed the audience about the Science Education Panel of IASc and the various activities undertaken by the Science Academies in the cause of science education, including the summer student scholarships, refresher programmes, lecture workshops, journal publications, etc. There were 6 academic sessions in all, 2 per day for 3 days. Each session comprised 2 ninety-minute lectures. Each of the 4 resource persons gave 1 lecture on each day. The details of the schedule and contents of the lectures are attached herewith.

2 The number of accepted applicants was 124, of whom 116 attended the Workshop. A Workshop kit was given to each participant. This comprised a spiral-bound 200 page note-book with a special cover design, a pen, a file folder and a copy of the Workshop schedule and lecture contents. The participants were particularly appreciative of the notebook and its cover design. All 12 lectures were of the blackboard-and-chalk kind. The material covered was explained unhurriedly, with careful emphasis on the basic principles of the subject, and with many worked out examples to illustrate these principles. Throughout the Workshop, the participation of the audience was commendable, with frequent interaction between the lecturer and the audience. Though the course was an intensive one, audience interest remained high for the entire duration. Questions and free-ranging discussions invariably spilled over into the breaks between lectures and beyond the end of the evening session. After the final lecture on the last day, there was a brief feedback session. Participants expressed their appreciation for the manner in which the Workshop had been organized and conducted. They expressed their gratitude to the Academies for sponsoring the workshop and thanked Loyola College for organizing the Workshop, and for making excellent arrangements for food and hospitality. Many participants requested that similar Lecture Workshops in the other subjects in the physics curriculum be held. Some teachers who participated in the Workshop also showed their interest in applying for and organizing similar Lecture Workshops in their colleges. Prof. V. Balakrishnan made brief concluding remarks, and urged interested students to go on to higher studies and research in physics.

3 Lecture Workshop on Classical Mechanics Loyola College, Chennai, 4-6 December 2014 Lecturers: Arul Lakshminarayan (AL), S. Lakshmi Bala (SLB), Suresh Govindarajan (SG) and V. Balakrishnan (VB). Time-table: Thursday, 4 December :00-09:30 Registration and Inauguration 09:30-11:00 Lecture 1 (VB) 11:00-11:20 Coffee break 11:20-12:50 Lecture 2 (SG) 12:50-14:00 Lunch break 14:00-15:30 Lecture 3 (AL) 15:30-15:50 Tea break 15:50-17:20 Lecture 4 (SLB) Friday, 5 December :30-11:00 Lecture 5 (VB) 11:00-11:20 Coffee break 11:20-12:50 Lecture 6 (SG) 12:50-14:00 Lunch break 14:00-15:30 Lecture 7 (AL) 15:30-15:50 Tea break 15:50-17:20 Lecture 8 (SLB) Saturday, 6 December :30-11:00 Lecture 9 (VB) 11:00-11:20 Coffee break 11:20-12:50 Lecture 10 (SG) 12:50-14:00 Lunch break 14:00-15:30 Lecture 11 (AL) 15:30-15:50 Tea break 15:50-17:20 Lecture 12 (SLB) 17:20-17:35 Concluding remarks 1

4 Objective: The main objective of this short but intensive Lecture Workshop was to help the participants develop an overall perspective of the general framework of classical dynamics, and of the Lagrangian and Hamiltonian formalisms in particular. The explicit working out of several appropriate physical examples was intended to aid this process. Detailed contents of lectures: Lectures 1, 5, 9 (VB) Classical mechanics in the general framework of dynamical systems. Autonomous and non-autonomous dynamical systems. Equations of motion. The role of initial conditions. Local solvability. Constants of the motion and integrability. The notions of phase space, phase trajectories, phase portrait. Flow in phase space. Conservative versus dissipative dynamical systems. Special case of a Hamiltonian system. Equilibrium points (or critical points) of a dynamical system. Flows in a two-dimensional phase space. Classification of critical points. Stability, asymptotic stability and instability. Linearization and linear stability analysis. Phase portraits of simple one-freedom systems. Extended phase space and timedependent constants of the motion. N-particle system with central forces and the 10 Galilean invariants. Lectures 2, 6, 10 (SG) Degrees of freedom. Constraints and independent degrees of freedom. Generalized coordinates and velocities. Lagrangian formalism of classical mechanics. Hamilton s action principle. Euler-Lagrange equations of motion. Role of initial conditions. Simple examples from mechanics. Cyclic coordinates and constants of the motion. Non-uniqueness of the Lagrangian. Invariance of the action under the addition of a total time derivative df/dt. Inclusion of constraints and non-inertial forces in the Lagrangian formalism: example of a bead on a rotating hoop. Phase portrait. Bifurcation to a new steady-state solution at a critical rotation frequency. Phase portrait of the simple pendulum. The role of separatrices. Lectures 3, 7, 11 (AL) Generalized momenta. Condition for the elimination of generalized velocities. Legendre transformation from the Lagrangian to the Hamiltonian. Hamilton s equations of motion. Constants of the motion and conservation laws in mechanics. Conservation of phase volume and Liouville s Theorem. Hamiltonian for a system of particles interacting by pairwise central potentials. Poisson brackets and canonically conjugate pairs of dynamical variables. Equation of motion for a general function of the dynamical variables. Canonical transformations. Gen- 2

5 erating functions and classification of canonical transformations. Time evolution as a sequence of canonical transformations. Action-angle variables. Liouville- Arnold integrability condition. Simple examples of integrable Hamiltonians. The double pendulum. Non-integrability and chaos. Lectures 4, 8, 12 (SLB) Two-body central force problem. Separation of centre-of-mass and relative coordinates. Conservation of total momentum. Transformation to spherical polar coordinates. Identification of radial and angular momentum variables. Conservation of angular momentum. Radial equation of motion. The Kepler problem and its natural scales. Constancy of the Laplace-Runge-Lenz vector. Special nature of the inverse square and harmonic potentials: Bertrand s Theorem. Scalar and vector potentials in electromagnetism. Lagrangian of a charged particle in an electromagnetic field. Derivation of the equation of motion and the Lorentz force. Gauge transformation of the electromagnetic potentials. Change in the Lagrangian under a gauge transformation. Invariance of the equation of motion under a gauge transformation. Canonical momentum and Hamiltonian of a charge particle in an electromagnetic field. Effect of a gauge transformation on the Hamiltonian. Lagrangian, Euler-Lagrange equation and acceleration of a relativistic charged particle in an electromagnetic field. Suggested reading: The literature on classical mechanics and dynamical systems is truly vast. Apart from specialised monographs on specific aspects of the subject, there are many excellent texts at the elementary, intermediate and advanced levels. A few of these texts are listed below, in order of increasing mathematical sophistication. D. T. Greenwood, Principles of Dynamics. J. B. Marion and S. T. Thornton, Classical Dynamics of Particles and Systems. V. Barger and M. Olsson, Classical Mechanics: A Modern Perspective. L. N. Hand and J. Finch, Analytical Mechanics. H. Goldstein, C. P. Poole and J. L. Safko, Classical Mechanics, 3rd edition. I. Percival and D. Richards, Introduction to Dynamics. L. D. Landau and E. M. Lifshitz, Mechanics. J. V. Jose and E. J. Saletan, Classical Dynamics: A Contemporary Perspective. V. I. Arnold, Mathematical Methods of Classical Mechanics, 2nd edition. 3

6 SCIENCE ACADEMIES Lecture workshop on CLASSICAL MECHANICS. (December 4 th, 5 th & 6 th 2014) - Organized by Dept. of Physics, Loyola college,chennai. Participants Details S.No College/Institutions No.of students participated 1. A.M.JAIN COLLEGE, CHENNAI 5 2. ETHIRAJ COLLEGE FOR WOMEN, CHENNAI L.N.GOVERNMENT COLLEGE, PONNERI 3 4. PACHAIYAPPA S COLLEGE, CHENNAI 9 5. PRESIDENCY COLLEGE, CHENNAI 4 6. QUEEN MARY S COLLEGE, CHENNAI 5 7. R.K.M.VIVEKANANDA COLLEGE, CHENNAI 8 8. MADRAS CHRISTIAN COLLEGE, CHENNAI 2 9. STELLA MARIS COLLEGE, CHENNAI WOMEN S CHRISTIAN COLLEGE, CHENNAI MADURAI KAMARAJ UNIVERSITY, MADURAI INDIRA GANDHI CENTRE FOR ATOMIC RESEARCH,KALPAKKAM VOORHEES COLLEGE, VELLORE VHNSN COLLEGE, VIRUDHUNAGAR IISER,THIRUVANANTHAPURAM KARUNYA UNIVERITY, COIMBTORE PONDICHERRY UNIVERSITY 1

7 18. KPR INSTITUTE OF ENGG & TECHNOLOGY, COIMBATORE CENTRAL UNIVERSITY OF TAMILNADU, THIRUVARUR GOVT ARTS COLLEGE, COIMBATORE GOVT ARTS COLLEGE, UDUMALPET, TIRUPPUR KONGUNADU ARTS AND SCIENCE COLLEGE, COIMBATORE SCHOOL TEACHERS DEPT OF NUCLEAR PHYSICS, UNIVERSITY OF MADRAS LOYOLA COLLEGE,CHENNAI SRI SANKARA ARTS & SCIENCE COLLEGE 1 Total 116

REPORT ON SCIENCE ACADEMIES LECTURE WORKSHOP ON SPONSORED & SUPPORTED BY. Indian Academy of Sciences, Bangalore. Organized by DEPARTMENT OF CHEMISTRY

REPORT ON SCIENCE ACADEMIES LECTURE WORKSHOP ON SPECTROSCOPIC TECHNIQUES AND APPLICATIONS TO CHEMICAL STRUCTURE ELUCIDATION 5 TH & 6 TH DECEMBER 2014 SPONSORED & SUPPORTED BY Indian Academy of Sciences,