Classical Mechanics Important Questions

Bsc/Msc Physics 

Unit 1: Newtonian Mechanics 

1. Explain Conservation laws of System.
2. What are Constraints? Disscus their classification.
3. What is Lagrangian function?
4. State and prove Principle of Virtual Work.
5. State and prove D Alembert's Principle in Generalised co-ordinates.
6. Derive Lagrange equation of motion from D Alembert  principle for Conservative or non conservative system.
7. What Are Configuration space?
8. Explain Hamilton principle.
9. Explain the deduction of Hamilton principle from the D Alembert principle.
10. Explain:- (i) Generalised coordinates. (ii) Transformation equation. (iii) Generalised displacement. (iv) Generalised velocity. (V) Generalised Acceleration. (Vi) Generalised force. (Vii) Generalised momentum.
11. Explain Conservation theorems of:- (i) Generalised momentum. (ii) Energy. (iii) Linear momentum. (iv) Angular momentum.
12. Explain:- (i) Differential Equation for the orbit. (ii) Equation of motion and first integral.
13. Define canonical transform. Derive the relation between old and new Hamiltonian. 

Unit 2

1. Deduce Hamiltonian Function.
2. Deduce Hamilton Canonical equations of motion.
3. Define generating function. Derive canonical transformation equation for the generating function (G2)
4. What are the physical significance of the Hamiltonian function?
5. Explain the Hamiltonian Jacobi action and angle variables.
6.  Define Poisson bracket and explain the equation of motion in the Poisson bracket.
7. State and prove Poisson equation theorem.
8. State and prove principle of least action. Deduce the principal of least action.
9. What is unbound motion?
10. Explain Rutherford scattering  cross section  in case of nucleon scattering.
11.  Disscus the Kepler's laws of planetary motion and problems.
12. What is inverse central force field?
13. Define Acceleration in rotating frame and coriolis force in rotating frame.

Unit 3

1. What are small oscillation? Obtain the Lagrangian equation of motion for small oscillation.
2.  Explain the theory of small oscillations with example.
3. Explain:-  (i) linear bistable molecule (ii) coriolis force and it's applications (iii) torque free motion of rigid body (iv) two coupled oscillator  (v)Explain Eular equation of motion for a rigid body.
4. What is stable and unstable equilibrium?

Unit 4

1. Explain:- (i) symmetries of space and time (ii)  invariance under galilion transformation (iii) covariant Four dimensional formulation 
2. Disscus Lorentz transformation equation. 
3. Explain :-  Fourier vector , four scaler , four momentum and four force.
4. Disscus the relativistic generalisation of Newton's law.
5. What are the postulates of special Theory of Relativity?
6. Differentiate between galilion and Lorentz transformation.
7. What is Minkowiski space?
8.  Explain covariant Lagrangian and Hamiltonian with examples.