Theoretical Mechanics

Description

Theoretical Mechanics Mir Publishers • Moscow 1970 Basic Definitions and Axioms of Statics 1. Fundamentals 3. Constraints and Their Reactions. Systems of Concurrent Forces in a Plane 4. Analytic Determination of the Resultant of 5. Resolution of a Force into Two Components P Q^> Ri P-QPix, (6) 9. Analytic Determination of the Resultant] of a System of Concurrent Forces (Method of Projections) 10. Conditions and Equations of Equilibrium for a System of Concurrent Forces 10 12. Theorem of Concurrence of Three Mutually Balanced Non-Parallel Forces Couple 14. Addition of Two Parallel Forces of Opposite Sense 15. Moment of a Couple 16. Equivalence of Couples. Translation of a Couple in Its Plane of Action 17. Theorem of Equivalent Couples 18. Addition of Couples Acting in the Same Plane Two-Dimensional Systems of Arbitrarily Located Forces 20. Equilibrium of a Lever SMo(P() = 0 (21) Q 21. Reduction of a Force to a Given Point 22. Reduction of a Two-Dimensional Force System to a Given Point 23. Resultant of a Two-Dimensional Force System 24. Theorem of the Moment of a Resultant (Varignon’s Theorem) Mo, = Mo~h Mo, = M0 4" Mo, (R'), 25. A Case of the Reduction of a Two-Dimensional Force System to a Couple 26. Conditions and Equations of Equilibrium for a Two-Dimensional Force System 27. Three Forms of Equilibrium Equations JL 30. Practical Solution of Equilibrium Problems for Two-Dimensional Force Systems QU 2-Ma = 0, tnA + Q-g-j- PI — 0. Ha = 0, 2Ma = 0, Pia + Q(-z + b)+P2(l-a)-VBl = 0, Friction 33. The Laws of Sliding Friction 34. Angle and Cone of Friction F = fQ, 35. Experimental Determination of Coefficients of Friction f°=^rtana o. (39) Three-Dimensional Force Systems 37. Force Parallelepiped 40. Equilibrium of an Arbitrary Three-Dimensional Force System R = 0, 1 Centroids and Centres of Gravity R = Pl~\- 44. Centroid of an Area. Static Moments of an Area 45. Centroid of a Line 46. Stability of Equilibrium Kinematics of Particles S = -g- [Uo + (Uo + 55. Kinematic Graphs and Relationship Between Them Simple Motions of Rigid Bodies ~KT • (110) 58. Velocities and Accelerations of Points of a Rotating Body Methods of Transmission of Rotary Motion 59. Classification of Transmission Mechanisms 60. Gear Ratio (120) (121b) 61. Cylinder Friction Drives (122) 63. Cone Friction Drives 64. Belt Drives: Fundamental Concepts 65. Gear Drives: General Considerations 67. Gear Trains V777X /It Y777A 68. Worm Gearing Complex Motion of Particles 69. Base, Relative and Absolute Motions 70. Theorems on Addition of the Velocities and Accelerations of a Particle in Complex Motion xr = fs(t) and yr = fi(t)- Plane Motion 7t. Concept of Plane Motion of a Rigid Body 72. Determination of the Velocity of Any Point of a Body in Plane Motion 73. Instantaneous Centre of Zero Velocity vA = o)/2, 74. Determination of the Acceleration of Any Point of a Body in Plane Motion 75. Planetary Gearing Basic Concepts and Axioms of Dynamics 78. Principle of Inertia 79. Fundamental Law of Dynamics of Particles 81. Axiom of Superposition 82. Axiom of Interaction 83. Two Basic Problems of Dynamics Motion of Particles. Method of Kinetostatics 85. D’Alembert’s Principle 86. Inertia Force for a Particle in Rectilinear Motion 87. Inertia Force for a Particle in Curvilinear Motion W = V(Wy + (W‘)*=l/ ^aiy+^a^y. (170) a a = V (a%)2 + {afA)2 = V (*>2P)a + («p)2 88. Inertia Force for a Rigid Body 89. Solution of Problems by the Method of Kinetostatics Work and Power 90. Work of a Constant Force in Rectilinear Motion 91. Work of a Variable Force in Curvilinear Motion 92. Work of a Resultant Force 93. Work of a Force of Gravity 94. Work of an Elastic Force , 96. Efficiency of a System of Mechanisms Connected in Series . (188) 99. Work and Efficiency for Bodies Sliding Along an Inclined Plane Work Done in Moving a Body Along an Inclined Plane. (200) F = Qf', r—J- 101. Work in Rolling Motion (212) (216) (220) U=.PS = Qf0S = Q^^S. (222) P = P' +