GENERAL ENGINEERING

By K. HIKAR

CONTENTS PART I KINEMATICS POINT KINEMATICS POINT VELOCITY AND ACCELERATION IN CARTESIAN COORDINATES DECOMPOSITION OF THE POINT VELOCITY AND ACCELERATION ALONG THE FRENET NATURAL TRIHEDRAL AXES VELOCITY OF A POINT IN CYLINDRICAL COORDINATES POINT VELOCITY IN SPHERICAL COORDINATES ARBITRARY CURVILINEAR POINT COORDINATES FUNDAMENTAL BASIS ELEMENTARY WORK RECIPROCAL BASIS CO- AND CONTRAVARIANT COMPONENTS OF THE VELOCITY VECTOR THE CONVENTION OF “RAISING AND LOWERING INDICES” CO- AND CONTRAVARIANT COMPONENTS OF THE ACCELERATION VECTOR THE LAGRANGE OPERATOR KINEMATICS OF THE RIGID SOLID COORDINATES OF A RIGID BODY THE EULER ANGLES VELOCITIES AND ACCELERATIONS OF POINTS OF A RIGID BODY IN THE CASE OF GENERAL MOTION ELEMENTAL TYPES OF THE MOTION OF A RIGID BODY ROTATION OF A RIGID BODY ABOUT A FIXED POINT PLANAR MOTION COMPOSITE MOTION COMPOSITE MOTION OF A PARTICLE PARTICLE VELOCITY UNDER BULK MOTIONS COMPOSITION OF MOTIONS OF A RIGID BODY KINEMATIC SCREW PART II DYNAMICS GENERAL ASPECTS OF RATIONAL MECHANICS FUNDAMENTALS OF ANALYTICAL MECHANICS PARTICLE DYNAMICS DIFFERENTIAL EQUATIONS OF PARTICLE MOTION IN VARIOUS COORDINATE SYSTEMS GENERAL PRINCIPLES OF PARTICLE DYNAMICS POTENTIAL FORCE FIELD DERIVATION OF THE LAGRANGE EQUATIONS OF THE SECOND KIND IN CASE OF NONSTATIONARY BASIS DERIVATION OF THE ENERGY INTEGRAL AND THE JACOBI INTEGRAL FROM THE LAGRANGE EQUATIONS OF THE SECOND KIND HAMILTON’S CANONICAL EQUATIONS OSCILLATORY MOTION OF A MASS POINT RELATIVE MOTION DYNAMICS OF A PARTICLE MOTION OF A PARTICLE SUBJECT TO CENTRAL FORCES SYSTEM DYNAMICS REPRESENTATIVE POINT ITS EQUATIONS OF MOTION THE PRINCIPLE OF LINEAR MOMENTUM AND THE PRINCIPLE OF MOTION OF THE CENTER OF MASS THE ANGULAR IMPULSE-MOMENTUM PRINCIPLE THE WORK-ENERGY PRINCIPLE OF A SYSTEM EQUILIBRIUM CONDITIONS OF A PARTICLE AND A SYSTEM CONSTRAINED MOTION I) CONSTRAINED MOTION OF A SYSTEM OF MATERIAL POINTS CONSTRAINED MOTION OF A POINT MOTION OF A MATERIAL POINT ON A SURFACE AND ON A LINE CONSTRAINED MOTION OF A SYSTEM OF MATERIAL POINTS CONSTRAINED MOTION OF A REPRESENTATIVE POINT THE LAGRANGE EQUATIONS EXAMPLES OF APPLICATIONS OF THE LAGRANGE EQUATIONS OF THE SECOND KIND THE MOTION EQUATIONS OF A NONHOLONOMIC SYSTEM OF MATERIAL POINTS IN THE GENERALIZED COORDINATES THE MAGGI EQUATIONS THE APPELL EQUATIONS FOR A SYSTEM OF MATERIAL POINTS II) CONSTRAINED MOTION OF GENERAL MECHANICAL SYSTEMS USE OF THE TANGENT SPACE IN THE STUDY OF THE CONSTRAINED MOTION OF GENERAL MECHANICAL SYSTEMS REACTION OF IDEAL CONSTRAINTS EQUATIONS OF THE CONSTRAINED MOTION OF GENERAL MECHANICAL SYSTEMS DERIVATION OF THE MOST USEFUL FORMS OF MOTION EQUATIONS OF NONHOLONOMIC SYSTEMS FROM THE MAGGI EQUATIONS MOTION CONTROL USING CONSTRAINTS DEPENDING ON THE PARAMETERS SMALL OSCILLATIONS OF SYSTEMS DIFFERENTIAL EQUATIONS OF SMALL MOTION AND THEIR INTEGRATION INVESTIGATION OF THE SMALL MOTION PATTERN OF SYSTEMS SMALL OSCILLATION OF A SYSTEM IN THE ABSENCE OF RESISTANCE FORCES PRINCIPAL COORDINATES MINIMUM-MAXIMUM PROPERTIES OF NATURAL FREQUENCIES SMALL OSCILLATION IN THE PRESENCE OF RESISTANCE FORCES AND GYROSCOPIC FORCES FORCED VIBRATION OF A MECHANICAL SYSTEM DYNAMICS OF THE RIGID SOLID DYNAMIC CHARACTERISTICS OF A RIGID SOLID DIFFERENTIAL EQUATIONS OF MOTION OF A FREE RIGID SOLID TRANSFORMATION OF FORCE SYSTEMS APPLIED TO A PERFECTLY RIGID SOLID EQUATIONS OF STATICS OF A RIGID SOLID ROTATION OF A RIGID SOLID AROUND A FIXED AXIS ROTATION OF A RIGID SOLID AROUND A FIXED POINT EQUATIONS OF MOTION OF A SYSTEM OF RIGID SOLIDS IN REDUNDANT (EXCESS) COORDINATES VARIATIONAL PRINCIPLES IN MECHANICS I) DIFFERENTIAL VARIATIONAL PRINCIPLES IN MECHANICS CLASSI?CATION OF THE MECHANICAL PRINCIPLES VIRTUAL DISPLACEMENTS OF MECHANICAL SYSTEMS THE D’ALEMBERT–LAGRANGE PRINCIPLE THE SUSLOV–JOURDAIN PRINCIPLE CHETAEV-TYPE CONSTRAINTS THE GENERALIZED D’ALEMBERT–LAGRANGE PRINCIPLE THE GAUSS PRINCIPLE UNIFORM VECTOR NOTATION AND GEOMETRIC INTERPRETATION OF DIFFERENTIAL VARIATIONAL PRINCIPLES II) INTEGRAL VARIATIONAL PRINCIPLES OF MECHANICS THE HAMILTON–OSTROGRADSKII PRINCIPLE THE LAGRANGE PRINCIPLE VARIOUS FORMS OF THE LAGRANGE PRINCIPLE ON THE VARIATIONAL PRINCIPLES OF MECHANICS THE HAMILTON–JACOBI EQUATION FOR THE FUNCTION STATICS EQUIVALENT SYSTEMS OF FORCES SYSTEMS OF PARALLEL FORCES THE CENTER OF MASS EQUILIBRIUM EQUATIONS SETTING UP AND SOLVING EQUILIBRIUM EQUATIONS EQUILIBRIUM OF TRUSSES EQUILIBRIUM FOR SYSTEMS WITH FRICTION EQUILIBRIUM OF A STRING INTEGRATION OF EQUATIONS IN MECHANICS HAMILTON–JACOBI THEOREM INTEGRAL INVARIANTS CANONICAL TRANSFORMATIONS OPTICAL-MECHANICAL ANALOGY ELEMENTS OF THE SPECIAL RELATIVITY THEORY KINEMATIC RELATIONS THE EQUATIONS OF DYNAMICS REFERENCES