Classical mechanics a textbook
Classical Mechanics begins with the Elementary Principles of Classical Mechanics and introduces the generalised coordinates, Lagrangian formulation and Hamiltonian Formulation and the Central Force used for derivation of Kepler's laws of planetary motion. The topic on Small Oscillations is intr...
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| Language: | English |
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Oxford, UK
Alpha Science International
2009
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Table of Contents:
- 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
- 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
- 8. Lagrangian and Hamiltonian for relativistic mechanics
- 9. Four-space
- 10. Problems and questions.