Classical mechanics: a textbook/
Suresh Chandra
- New Delhi: Narosa Publication House, 2009.
- x, 334 p. : ill. ; 25 cm.
I. Elementary Principles. -- 1. Inertial reference frame -- 2. Newton laws of motion -- 3. Linear motions -- 4. Forces in classical mechanics -- 5. Maxwell equations -- 6. Motion of a charged particle in electromagnetic eld [i.e. field] -- 7. Galilean transformations -- 8. Conservative and non-conservative forces -- 9. Mechanics of a single particle -- 10. Mechanics of a system of particles -- 11. Motion in a resistive medium -- 12. Constraints -- 13. Generalized coordinates and degrees of freedom -- 14. Virtual displacement and virtual work -- 15. D'Alembert's principle -- 16. Problems and questions -- II. Lagrangian Formulation. -- 1. Lagrangian equation of motion -- 2. Variation technique -- 3. Kinetic energy in terms of generalized coordinates -- 4. Jacobi integral -- 5. Dissipative system: Rayleigh's dissipation function -- 6. Gauge transformation for Lagrangian -- 7. Symmetry properties and conservation laws -- 8. Invariance of Lagrangian equations under Galilean transformation -- 9. Variational principle -- 10. Problems and questions -- III. Hamiltonian Formulation. -- 1. Hamiltonian equations of motion -- 2. Derivation of Hamiltonian equations from the variational principle -- 3. Principle of least action -- 4. Canonical transformations -- 5. Maxwell type relations -- 6. Poisson brackets -- 7. Hamilton-Jacobi method -- 8. Problems and questions -- IV. Central Force. -- 1. Reduction of two-body problem into one-body problem -- 2. Central force -- 3. Kepler's laws -- 4. Rutherford scattering -- 5. Virial theorem -- 6. Problems and questions -- V. Small Oscillations. -- 1. Stable and unstable equilibriums -- 2. Small oscillations in a system with one degree of freedom -- 3. Small oscillations in a system with more than one degree of freedom -- 4. Normal coordinates and normal frequencies of vibration -- 5. Problems and questions -- VI. Rigid-body Dynamics. -- 1. Rotating frame -- 2. Euler angles -- 3. Inertia tensor -- 4. Euler's equations of motion of a rigid body -- 5. Free motion of a rigid body -- 6. Motion of a symmetric top -- 7. Problems and questions -- VII. Special Relativity. -- 1. Galilean transformations -- 2. Michelson-Morley experiment -- 3. Special theory of relativity -- 4. Lorentz transformations -- 5. Variation of mass with velocity -- 6. Mass-energy equivalence -- 7. Relativistic Doppler eect [i.e. effect] -- 8. Lagrangian and Hamiltonian for relativistic mechanics -- 9. Four-space -- 10. Problems and questions.