Specific Objectives of course:
To provide solid understanding of classical mechanics and enable the students to use this understanding while studying courses on quantum mechanics, statistical mechanics, electromagnetism, fluid dynamics, space-flight dynamics, astrodynamics and continuum mechanics.
Rectilinear motion of particles. Uniform rectilinear motion, uniformly accelerated rectilinear motion. Curvilinear motion of particle, rectangular components of velocity and acceleration. Tangential and normal components. Radial and transverse components. Projectile motion.
Work, power, kinetic energy, conservative force fields.
Conservation of energy, impulse, torque. Conservation of linear and angular momentum. Non-conservative forces.
Simple Harmonic Motion:
The simple harmonic oscillator, period, frequency. Resonance and energy. The damped harmonic oscillator, over damped, critically damped and under damped. Motion, forces and vibrations.
Central Forces and Planetary Motion:
Central force fields, equations of motion, potential energy, orbits. Kepler’s law of planetary motion. Apsides and apsidal angles for nearly circular orbits. Motion in an inverse square field.
Planer Motion of Rigid Bodies:
Introduction to rigid and elastic bodies, degree of freedom, translations, rotations, instantaneous axis and center of rotation, motion of the center of mass. Euler’s theorem and Chasles’ theorem. Rotation of a rigid body about a fixed axis, moments and products of inertia. Parallel and perpendicular axis theorem.
Motion of Rigid Bodies in Three Dimensions:
General motion of rigid bodies in space. 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. The Eulerian angles, angular velocity and kinetic energy in terms of Euler angles. Motion of a spinning top and gyroscopes-steady precession, sleeping top.