Theoretical Mechanics

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-Q 6. Addition of Concurrent Forces in a Plane.
R = Rz-\-Pi = PiJrP2-\-Pz-\- Pi-
8. Projection of a Vector Sum on an Axis
Rx=f>Pix, (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' + <7,
The Laws of Dynamics
Pz.
107. Moments of Inertia of Homogeneous Bodies of Simple Shape
109. Law of Kinetic Energy for a System of Particles
4!-4
110. Fundamental Equation of Dynamics for a Rigid Body in Rotation
%M = fQR.
_2A<°
Application of the Laws of Kinematics and Dynamics to the Analysis of Mechanisms*
112. Fundamentals of Kinematics of Mechanisms
114. Distribution of Accelerations in a Body in Plane Motion
ab = aA\
Um-f Uu f-\-Up-f-
SUBJECT INDEX