Annamalai University 2008-1st Year M.Sc Mathematics Analytical Mechanics and Theory of relativity - - Question Paper

2.    For a rotating frame, prove that the rate of change of a vector is equal to the rate of growth plus the rate of transport.

3.    What is Jacobian elliptic function? State its properties;

4.    Explain Ferels law.

5.    Explain the Eulerian angles and find an expression for the angular velocity.

6.    Describe the spinning top.

7.    Explain the classification of dynamical systems.

8.    Explain Lagranges equation for impulsive motion.

9.    State the postulates of special theory of relativity.

10.    Derive the mass - energy equivalence.

SECTION - B (3 x 20 = 60)

Answer any THREE questions.

Each question carries TWENTY marks.

11.    (a) State and prove the principle of

conservation of energy.

(b) Derive the expression for the angular momentum of a rigid body.

12.    (a) Discuss the motion of a simple pendulum.

(b) Find the equation of motion of a charged particle in uniform electric and magnetic fields which are perpendicular to each other.

13.    (a) Discuss the motion of a rolling disk.

(b) Discuss the motion of a billiard ball.

14.    (a) Establish Lagranges equations of motion

of a particle in a plane.

(b) State and prove Hamiltons principle.

15.    (a) Explain the concept of Lorentz

contraction.

(b) Explain time dilation.