MechanicsSince mechanics is the science of motion, studies in this field now cover a wider range of problems than has been the case in earlier classical approaches. This has been achieved by the inclusion of aspects relating to the mechanics of continuous media, or strength problems. The topics covered in this book present a comprehensive treatment of the subject providing a broader perspective to the meaning of mechanics, in the modern sense of the word.Problems in the areas of strength of materials, hydromechanics and theory of elasticity are examined. The author has also endeavoured to show a certain universality of some methods seemingly specific to mechanics by tackling some problems involving electrical or electromechanical systems but based on Lagrange's equations.The book has been designed to emphasize that mechanics is a deductive system, where the aim is not only to present mechanics as the science of motion but also to show that it serves as a bridge between mathematics and its applications, in the broadest sense of the word. Mechanical problems have inspired great mathematicians to come to grips with new mathematical problems, an excellent example here being the problem of the brachistochrone which initiated the development of the variational calculus. The book gives a comprehensive overview on new theoretical findings, and gives many applications which will prove indispensable to all those interested in mechanical and allied problems. |
Contents
Introduction | 1 |
Kinematics of a Particle | 26 |
Kinematics of a Body | 53 |
Copyright | |
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Common terms and phrases
a₁ angular momentum angular velocity assume axis axode C₁ C₂ centre of mass coefficients components considered constant constraints contravariant coordinates cosy covariant curvilinear curvilinear coordinates defined degrees of freedom denote derivative determined differential equation displacements dt dt elastic equation of motion equilibrium Example expressed Əqi follows frame of reference function harmonic oscillator Hence holonomic systems inertia instantaneous centre integral kinematic pairs kinetic energy Kronecker delta linear m₁ m₂ matrix mechanics metric tensor moment of inertia moving number of degrees obtain orthogonal Oxyz P₁ particle plane position vector potential energy problem reference origin right-hand side rigid body rotation Section side of equation Skalmierski solution space stability straight line stress Substituting surface theorem trajectory transformation V₁ vibrations viscoelastic w₁ write X₁ ΕΙ ӘЕ ән ду