- 11 students
- 3 lessons
- 22 quizzes
- 10 week duration
This Course is based on the M.Sc Physics syllabus of St. Albert’s College (Autonomous) and M.G. University.
Syllabus : LECTURE#2_About the course_PPH1CRT0219
Objective of the course:
After completing the course, the students will
(i) understand the fundamental concepts of the Lagrangian and the Hamiltonian methods and will be able to apply them to various problems;
(ii) understand the physics of small oscillations and the concepts of canonical transformations and Poisson brackets ;
(iii) understand the basic ideas of central forces and rigid body dynamics;
(iv) understand the Hamilton-Jacobi method and the concept of action-angle variables. This course aims to give a brief introduction to the Lagrangian formulation of relativistic mechanics.
Recommended Text Books
1. Classical Mechanics: Herbert Goldstein , Charles Poole and John Safko, (3/e); Pearson Education.
2.Classical Mechanics: G. Aruldhas, Prentice Hall 2009.
1. Theory and Problems of Theoretical Mechanics (Schaum Outline Series): Murray R. Spiegel, Tata McGraw-Hill 2006.
2. Classical Mechanics : An Undergraduate Text: Douglas Gregory, Cambridge University Press.
3. Classical Mechanics: Tom Kibble and Frank Berkshire, Imperial College Press.
4. Classical Mechanics ( Course of Theoretical Physics Volume 1): L.D. Landau and E.M. Lifshitz, Pergamon Press.
5. Analytical Mechanics: Louis Hand and Janet Finch, Cambridge University Press.
6. Classical Mechanics: N.C.Rana and P. S. Joag, Tata Mc Graw Hill.
7. Classical Mechanics: J.C. Upadhyaya, Himalaya Publications, 2010.
- Tutorial #1 : Review of Newtonian Mechanics: Mechanics of a Particle; Mechanics of a System of Particles.
- Degrees of Freedom and Constraints
- Determine the Degrees of freedom in the following cases. Give the equation of the constraint in each case.
- Classification of dynamical System
- Determine whether the following systems are holonomic or nonholonomic. Specify the constraint force in each case
- Co-ordinate systems
- Generalized coordinates
- Principle of virtual work
- D’Alembert principle
- Lagrange’s equation from D’Alembert principle
- Application of Lagrange’s equation
- Application of Lagrange’s equation to: motion of a single particle in Cartesian coordinate system
- Application of Lagrange’s equation to: motion of a single particle in plane polar coordinate system
- Application of Lagrange’s equation : bead sliding on a rotating wire
- Solve the Problems using Lagrange’s equation of motion.
- velocity-Dependent potentials and the Dissipation Function
- Application of Lagrange’s equation : Lagrangian for a charged particle in electromagnetic field
- Cyclic coordinates and Conjugate momentum
- Calculus of variation
- The Brachistochrone Problem
- Hamilton’s Principle; Technique of Calculus of variations and Derivation of Lagrange’s equations from Hamilton’s Principle
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