Unit-I Review of Basic Force Systems: Dimensions and units of mechanics, idealization
of mechanics, laws of mechanics, vector algebra review, moment of a force about a
point and axis, the couple and couple moment, addition and subtraction of couples,
moment of a couple about a line, translation of a force to a parallel position, resultant
of a force system, Problems (vector method).
Unit-II Equilibrium: Introduction, free body diagram, control volumes, general equations of
equilibrium, two point equivalent loading, static in-determinacy, simple truss, method
of joints, method of sections, co-planer cable-loading a function of x, coplanar
cables- loading the weight of the cable itself. Problems.
Unit-III Properties of Surfaces & Moments and Products of inertia : First moment of an
area and the centroid, principal axes, formal definition of inertia quantities, relation
between mass-inertia terms and area-inertia terms, translation of coordinate axes,
transportation properties of the inertia terms, a brief introduction to tensors, the inertia
of ellipsoid and principal moments of inertia, Problems (vector method).
Unit-IV Kinematics of Particles and Rigid Bodies: Velocity and acceleration in path and
cylindrical coordinates, motion of a particle relative to a pair of translating axes,
translation and rotation of rigid bodies, Chasles theorem, moving references,
velocity and acceleration for different references, inertia and coriolis forces.
Problems(vector method).
Unit-V Particle Dynamics, Energy Methods & Momentum Methods: Newton's law for
rectangular coordinates & cylindrical coordinates, rectifier translation, central
force motion, Newton's law for path variables, work energy equations, work energy
equations for a systems of particles, linear and angular momentum equations for a systems
of particles. Problems(vector method).
Unit-VI Variational Mechanics: Hamiton principle, Lagrange equations, principle of virtual
work, methods of minimum potential energy, stability.