DYNAMICS OF A RIGID BODY
D'Alembert's principle. The general equations of motion of a rigid body. Motion of centre of inertia and motion relative to centre of inertia. Motion about a fixed axis: Finite forces (Moment of effective forces about a fixed axis of rotation, angular momentum, kinetic energy of a rotating body about a fixed line. Equation of Motion of the body about the Axis of Rotation, Principle of Conservation of energy.The compound pendulum (Time of a Complete Oscillation,Minimum time of oscillation), Centre of percussion.
Motion of a rigid body in two dimensions:Equations of motion in two dimensions,Kinetic energy of a rigid body, Moment of Momentum, Rolling and sliding Friction, Rolling of a sphere on a rough inclined plane , Sliding of a Rod, Sliding and Rolling of a Sphere on an inclined plane, Sliding and Rolling of a sphere on a fixed sphere. Equations of motion of a rigid body under impulsive forces, Impact of a rotating Elastic sphere on a fixed horizontal Rough plane. Change in K.E. due to the action of impulse.
Motion in three dimensions with reference to Euler's dynamical and geometrical equations. Motion under no forces, Motion under impulsive forces. Conservation of momentum (linear and angular) and energy for finite as well as impulsive forces.
Lagrange's equations for holonomous dynamical system, Energy equation for conservative field, Small oscillations, Motion under impulsive forces. Motion of a top.
Hamilton's equations of motion, Conservation of energy, Hamilton's principle and principle of least action.
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