Detailed Syllabus
Ch 1. Fundamental Concepts: Vectors
1)
Vector
Properties
2)
Scalar
& Vector Product
3)
Vector
Addition
4)
Unit
Victors and Directional cosines
5)
Vector Calculus
6)
Gradient,
divergence and Curl
7)
Co-ordinate
transformations
8)
Velocity
and acceleration in plane polar, cylindrical and spherical co-ordinates
Ch 2. Newtonian Mechanics
1)
Dimensions
& Units
2)
Newton’s
Laws and Inertial Systems
3)
Applications
of Newton’s Laws
4)
Constant
applied forces
5) Time
dependent forces
6)
Velocity
dependent forces
7)
Position
dependent forces (Conservative. Potential Energy)
8)
Linear restoring force
9)
Variation of gravitational field
Ch 3. Harmonic Oscillator
1)
Linear
and nonlinear oscillation
2)
Linear
harmonic oscillator
3)
Damped
harmonic oscillator (Critical, under damp, over damp)
4)
Quality
factor
5)
Driven
(forced harmonic) oscillator
6)
Resonance
– amplitude, energy
7)
Rate of
energy dissipation
8)
Harmonic
motion in 2- D (Details in Ch 4)
9)
Harmonic
oscillation in electrical circuits
10)
Fourier
series and superposition principle
11)
Green’s
function and harmonic motion
12)
Impulsive force
Ch
4. Motion in 2 and 3 D
1)
Dynamic
in 3- D
2)
Torque
3)
Harmonic Oscillator in 2 and 3 D
4)
Projectile
motion
5)
Motion of Charged Particles in Electric and Magnetic Fields
6)
Constrained Motion of a Particle
Ch 6. Central force and gravitation
1)
Central
force and potential energy
2)
Central
force motion as a one body problem
3)
The law
of Ellipses (Kepler’s first law)
4)
The law
of areas (Kepler’s second law)
5)
The
harmonic law (Kepler’s third law)
6)
Central
force field orbits and effective Potential
7)
Orbits in
an inverse square force field
8)
Orbital
transfers, gravitational boost
Ch 7. System of particles
1)
Center of
mass and linear momentum of a system
2)
Angular
momentum and kinetic energy
3)
Reduced
mass
4)
Conservation
of energy, momentum
5)
Variable
mass systems – rocket propulsion
6)
Elastic
collision and conservation laws
7)
Inelastic
collisions
Ch 8. Rigid body motion
1)
Center of
mass of rigid body
2)
Rotation
about an axis
3)
Moment of inertia
4)
Impulse and Collisions Involving Rigid Bodies
Ch10. Lagrangian and Hamiltonian Dynamics
1)
Generalized co-ordinates and constraints
2)
Generalized
forces
3)
Lagrange’s
equation of motion for a single particle and a system of particle
4)
Hamiltonian
variational principle
Ch 11. Theory of
small oscillations
1) Potential Energy and
Equilibrium. Stability
2) Oscillation of a system with
One Degree of Freedom about a position of Stable Equilibrium
3) Coupled Harmonic
Oscillators. Normal Coordinates
4) General Theory of
Vibrating Systems
5) Vibration of a Loaded
String of Linear Array of Coupled Harmonic Oscillators
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