THE ECONOMY OF WORKSHOP MANIPULATION: LOGICAL METHOD FOR LEARNING CONSTRUCTIVE MECHANICS
CONTENTS PART I KINEMATICS 1 POINT KINEMATICS 3 1 POINT VELOCITY AND ACCELERATION IN CARTESIAN COORDINATES 3 2 DECOMPOSITION OF THE POINT VELOCITY AND ACCELERATION ALONG THE FRENET NATURAL TRIHEDRAL AXES 6 3 VELOCITY OF A POINT IN CYLINDRICAL COORDINATES 11 4 POINT VELOCITY IN SPHERICAL COORDINATES 13 5 ARBITRARY CURVILINEAR POINT COORDINATES FUNDAMENTAL BASIS 15 6 ELEMENTARY WORK RECIPROCAL BASIS 17 7 CO AND CONTRAVARIANT COMPONENTS OF THE VELOCITY VECTOR THE CONVENTION OF RAISING AND LOWERING INDICES 20 8 CO AND CONTRAVARIANT COMPONENTS OF THE ACCELERATION VECTOR THE LAGRANGE OPERATOR 23 2 KINEMATICS OF THE RIGID SOLID 29 1 COORDINATES OF A RIGID BODY THE EULER ANGLES 29 2 VELOCITIES AND ACCELERATIONS OF POINTS OF A RIGID BODY IN THE CASE OF GENERAL MOTION 34 3 ELEMENTAL TYPES OF THE MOTION OF A RIGID BODY 37 4 ROTATION OF A RIGID BODY ABOUT A FIXED POINT 39 5 PLANAR MOTION 44 3 COMPOSITE MOTION 49 1 COMPOSITE MOTION OF A PARTICLE 49 2 PARTICLE VELOCITY UNDER BULK MOTIONS 53 3 COMPOSITION OF MOTIONS OF A RIGID BODY 55 4 KINEMATIC SCREW 60 PART II DYNAMICS GENERAL ASPECTS OF RATIONAL MECHANICS FUNDAMENTALS OF ANALYTICAL MECHANICS 4 PARTICLE DYNAMICS 73 1 DIFFERENTIAL EQUATIONS OF PARTICLE MOTION IN VARIOUS COORDINATE SYSTEMS 73 2 GENERAL PRINCIPLES OF PARTICLE DYNAMICS 76 3 POTENTIAL FORCE FIELD 83 4 DERIVATION OF THE LAGRANGE EQUATIONS OF THE SECOND KIND IN CASE OF NONSTATIONARY BASIS 92 5 DERIVATION OF THE ENERGY INTEGRAL AND THE JACOBI INTEGRAL FROM THE LAGRANGE EQUATIONS OF THE SECOND KIND 95 6 HAMILTON S CANONICAL EQUATIONS 97 7 OSCILLATORY MOTION OF A MASS POINT 100 8 RELATIVE MOTION DYNAMICS OF A PARTICLE 110 9 MOTION OF A PARTICLE SUBJECT TO CENTRAL FORCES 116 5 SYSTEM DYNAMICS 143 1 REPRESENTATIVE POINT ITS EQUATIONS OF MOTION 143 2 THE PRINCIPLE OF LINEAR MOMENTUM AND THE PRINCIPLE OF MOTION OF THE CENTER OF MASS 150 3 THE ANGULAR IMPULSE MOMENTUM PRINCIPLE 151 4 THE WORK ENERGY PRINCIPLE OF A SYSTEM 157 5 EQUILIBRIUM CONDITIONS OF A PARTICLE AND A SYSTEM 163 6 CONSTRAINED MOTION 167 I CONSTRAINED MOTION OF A SYSTEM OF MATERIAL POINTS 168 1 CONSTRAINED MOTION OF A POINT 168 2 MOTION OF A MATERIAL POINT ON A SURFACE AND ON A LINE 172 3 CONSTRAINED MOTION OF A SYSTEM OF MATERIAL POINTS CONSTRAINED MOTION OF A REPRESENTATIVE POINT THE LAGRANGE EQUATIONS 190 4 EXAMPLES OF APPLICATIONS OF THE LAGRANGE EQUATIONS OF THE SECOND KIND 204 5 THE MOTION EQUATIONS OF A NONHOLONOMIC SYSTEM OF MATERIAL POINTS IN THE GENERALIZED COORDINATES THE MAGGI EQUATIONS 220 6 THE APPELL EQUATIONS FOR A SYSTEM OF MATERIAL POINTS 233 II CONSTRAINED MOTION OF GENERAL MECHANICAL SYSTEMS 239 7 USE OF THE TANGENT SPACE IN THE STUDY OF THE CONSTRAINED MOTION OF GENERAL MECHANICAL SYSTEMS 239 8 REACTION OF IDEAL CONSTRAINTS 244 9 EQUATIONS OF THE CONSTRAINED MOTION OF GENERAL MECHANICAL SYSTEMS 247 10 DERIVATION OF THE MOST USEFUL FORMS OF MOTION EQUATIONS OF NONHOLONOMIC SYSTEMS FROM THE MAGGI EQUATIONS 265 11 MOTION CONTROL USING CONSTRAINTS DEPENDING ON THE PARAMETERS 279 7 SMALL OSCILLATIONS OF SYSTEMS 293 1 DIFFERENTIAL EQUATIONS OF SMALL MOTION AND THEIR INTEGRATION 293 2 INVESTIGATION OF THE SMALL MOTION PATTERN OF SYSTEMS 299 3 SMALL OSCILLATION OF A SYSTEM IN THE ABSENCE OF RESISTANCE FORCES 302 4 PRINCIPAL COORDINATES 308 5 MINIMUM MAXIMUM PROPERTIES OF NATURAL FREQUENCIES 311 6 SMALL OSCILLATION IN THE PRESENCE OF RESISTANCE FORCES AND GYROSCOPIC FORCES 317 7 FORCED VIBRATION OF A MECHANICAL SYSTEM 322 8 DYNAMICS OF THE RIGID SOLID 327 1 DYNAMIC CHARACTERISTICS OF A RIGID SOLID 327 2 DIFFERENTIAL EQUATIONS OF MOTION OF A FREE RIGID SOLID 339 3 TRANSFORMATION OF FORCE SYSTEMS APPLIED TO A PERFECTLY RIGID SOLID 341 4 EQUATIONS OF STATICS OF A RIGID SOLID 345 5 ROTATION OF A RIGID SOLID AROUND A FIXED AXIS 347 6 ROTATION OF A RIGID SOLID AROUND A FIXED POINT 350 7 EQUATIONS OF MOTION OF A SYSTEM OF RIGID SOLIDS IN REDUNDANT EXCESS COORDINATES 371