An Introduction to MechanicsThis text describes advanced studies in applied mathematics and applied physics. The text includes a discussion of vector analysis followed by its applications in particle mechanics and mechanics of rigid bodies. Each chapter contains solved problems and examples which help to illustrate the principles discussed in the chapter. The last two chapters deal with Lagrange's theorem and Hamilton's theorem and their applications in calculus of variations - a mathematical tool, needed in the study of applied mathematics and applied physics. |
Contents
Introduction | 1 |
Differentiation and Integration of Vectors | 33 |
Gradient Divergence and Curl | 53 |
Integral Theorem | 69 |
Rectilinear Motion | 99 |
33 | 110 |
Plane Kinematics | 121 |
Moments and Stability of Equilibrium | 139 |
53 | 237 |
Moment of Inertia | 248 |
Impulsive Motion | 274 |
The Equation of Lagrange and Hamilton | 305 |
Calculus of Variation | 311 |
Theory of Curves | 325 |
Theory of Surfaces and Curvilinear Coordinates | 359 |
Curves on a Surface | 390 |
Work and Energy | 158 |
Centre of Gravity | 179 |
Friction | 194 |
Motion of a Particle | 214 |
Projectile | 232 |
| 416 | |
| 417 | |
| 418 | |
Common terms and phrases
acceleration angle applied axis becomes centre centre of gravity components condition Consider constant coordinate cos² couple curvature curve denotes derivatives differential equation direction displacement distance dv² earth equal equation of motion equilibrium EXAMPLE expression external forces Find fixed force friction function given Hence horizontal impact implies impulsive inertia initial integration kinetic energy length linear magnitude mass mass centre moment moving normal obtained origin parallel parameter parametric curves particle perpendicular plane position vector principal projected projectile Proof Prove putting r₁ r₂ radius represents respect rest resultant rigid body scalar Show sides Similarly simple sin² smooth Solution sphere string Suppose surface tangent theorem velocity vertical weight zero ду