NOTE: Attempt any FIVE questions selecting at least TWO questions from each section.

Section-I (5/9)

Vector Integration

•    Line integrals

•    Surface area and surface integrals

•    Volume integrals

Integral Theorems

•    Green’s theorem

•    Gauss divergence theorem

•    Stoke’s theorem

Curvilinear Coordinates

•    Orthogonal coordinates

•    Unit vectors in curvilinear systems

•    Arc length and volume elements

•    The gradient, Divergence and curl

•    Special orthogonal coordinate systems

Tensor Analysis

•    Coordinate transformations

•    Einstein summation convention

•    Tensors of different ranks

•    Contravariant, Covariant and mixed tensors

•    Symmetric and skew symmetric tensors

•    Addition, Subtraction, Inner and outer products of tensors

•    Contraction theorem, Quotient law

•    The line element and metric tensor

•    Christoffel symbols



Section-II (4/9)

Non Inertial Reference Systems

•    Accelerated coordinate systems and inertial forces

•    Rotating coordinate systems

•    Velocity and acceleration in moving system: Coriolis, Centripetal and transverse acceleration

•    Dynamics of a particle in a rotating coordinate system

Planar Motion of Rigid Bodies

•    Introduction to rigid and elastic bodies, Degrees of freedom, Translations, Rotations, instantaneous axis and center of rotation, Motion of the center of mass

•    Euler’s theorem and Chasle’s theorem

•    Rotation of a rigid body about a fixed axis:  Moments and products of inertia of various bodies including hoop or cylindrical shell, circular cylinder, spherical shell

•    Parallel and perpendicular axis theorem

•    Radius of gyration of various bodies

Motion of Rigid Bodies in Three Dimensions

•    General motion of rigid bodies in space:    Moments and  products  of  inertia,  Inertia matrix

•    The momental ellipsoid and equimomental systems

•    Angular momentum vector and rotational kinetic energy

•    Principal axes and principal moments of inertia

•    Determination of principal axes by diagonalizing the inertia matrix

Euler Equations of Motion of a Rigid Body

•    Force free motion

•    Free rotation of a rigid body with an axis of symmetry

•    Free rotation of a rigid body with three different principal moments

•    Euler’s Equations

•    The Eulerian angles,  Angular velocity and kinetic energy in terms of Euler angles, Space cone

•    Motion of a spinning top and gyroscopes- steady precession, Sleeping top