Week 1:
Objective of classical mechanics, classical mechanics as a dynamical
theory, Newton’s laws of motion, conservation of linear momentum, angular
momentum and energy, work done, work-energy principle
Week 2:
Conservative and non-conservative force fields, concept of potential,
Stable and unstable equilibria, analysis of motion using energy diagram
Week 3:
Velocity and acceleration in polar coordinates; Motion under central
forces, effective potential energy, finding trajectory for a given force
law and vice-versa
Week 4:
Kepler’s problem, Laplace Runge-Lenz vector, Rutherford scattering
Week 5:
Linear harmonic oscillator with and without forcing, resonance, damped
harmonic oscillator without forcing
Week 6:
Damped harmonic oscillator with forcing, condition of resonance; Motion of
a particle in the presence of electric and magnetic fields
Week 7:
Galilean transformation, inertial and non-inertial frames of references,
relation between the time derivatives of an inertial and a non-inertial
frame, pseudo forces
Week 8:
Motion of a particle under constraints, classification of constraints;
principle of virtual work
Week 9:
Generalized coordinates and generalized velocities;
Euler-Lagrange’s equations from D’alembert’s principle, cyclic coordinates
Week 10:
Properties of Lagrangian, application to constrained motions of a single
particle
Week 11:
Concept of phase space, fixed points and linear stability analysis
Week 12:
Conservative vs. nonconservative systems, attractors, chaos in
conservative and nonconservative systems
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