Theoretical Mechanics A Short Course/

Table of Content

Part 1 Statics of rigid bodies
Chapter 1 Basic concepts and principles
The subject of statics
Force Fundamentals of principles
Constraints and their reactions
Axiom of constraints

Chapter 2 Composition of forces Concurrents force systems
Geometrical method of composition of forces resultant of concurrent forces
Resolution of forces
Projection of a force on an axis and on a plane
Analytical method of defining a force
Analytical method of composition of forces
Etc.

Chapter 3 Parallel forces and force couples in a plane
Composition and resolution of parallel forces
A force couple, moment of a couple
Equivalent couples
Composition of coplanar couples, conditions for the equilibrium of couples

Chapter 4 General case of forces in a plane
Theorem of translation of a force
Reduction of coplanar force system to a given center
Reduction of coplanar force system to the simplest possible from
Conditions for the equilibrium of a coplanar force system. the case of parallel forces
Solution of problems
Etc.

Chapter 5. Elements of Graphical statics
Force and string polygons. reduction of a coplanar force system to two forces
Graphical determination of a resultant
Graphical determination of a resultant couple
Graphical conditions of equilibrium of a coplanar force system
Determination of the reactions of constraints

Chapter 6 Solution of Trusses
Trusses. Analytical analysis of plane trusses
Graphical analysis of a plane trusses
The Maxwell -Cremona diagram

Chapter 7 Friction
Laws of state friction
Reactions of rough constraints, angle of friction
Equilibrium with friction
Belt friction
Rolling friction and pivot friction

Chapter 8 Couples and forces in space
Moment of a force about a point as vector
Moment of a force with respect to an axis
Relation between the moments of a force about a point and an axis
Vector expression of the moment of a couple
Composition of couples in space. conditions

Chapter 9 Center of Gravity
Center of parallel forces
Center of gravity of a rigid body
ordinates of center of gravity of homogeneous bodies
Methods of determining the ordinates of the center of gravity of bodies
Centers of gravity of some homogeneous bodies

Part 2 Kinematics of a particle and a rigid body
Chapter 10. Kinematics of a particle
Introduction to kinematics
Methods of describing motion of a particle. Path
Conversion from coordinate to natural method of describing motion
Velocity vector of a particle
Etc.

11 Transnational and rotational motion of rigid body
Translation motion
Rotational motion of a rigid body, Angular velocity and angular accelerations
Uniform and uniformly variable rotations
Velocities and accelerations of the points of a rotating body

Chapter 12 Plane motion of rigid body
Equations of plane motion. resolution of motion into translation and rotation
Determination of the Path of a point of a body
Determination of the velocity of a point of a body
Theorem of the projections of the velocities of two points of a body
Etc.

Chapter 13. Motion of a rigid body having one fixed point and motion of a free rigid body
Motion of a rigid body having one fixed point
Velocity and acceleration of a point of a body
The general motion of a free rigid body

Chapter 14. Resultant motion of a particle
Relative, transport, ans absolute motion
Composition of velocities
Composition of problems

Chapter 15 Resultant motion of a rigid body
Composition of transnational motions
Composition of rotations about two parallel axes
Toothed spur gearing
Composition of rotations about intersecting axes
Euler kinematic equations

Chapter 16. Introduction of dynamics. Laws of dynamics
Chapter 17. Differential equations of motion for a particle and their integration
Chapter 18. General theorems of particle dynamics
Chapter 19. Constrained motion of a particle
Chapter 20. Relative motion of a particle
Chapter 21. Rectilinear vibration of a particle
Chapter 22 Motion of a body in the earth's gravitational field
Chapter 23. Introduction to the dynamics of a system. Moments of Inertia of rigid bodies
Chapter 24. Theorem of the motion of the Centre of mass of a system
Chapter 25. Theorem of the change in the linear momentum of s stems
Chapter 26. Theorem of the change in the angular
Chapter 27. Theorem of the change in the kinetic energy of a system
Chapter 28 Applications of the general theorems to rigid-body dynamics
Chapter 29. Applications of the general theorems to the theory of impact
Chapter 30. D' Alembert's principle, Forces acting on the axis of a rotating body
Chapter 31. The principle of virtual displacements and the general equation of dynamics
Chapter 32. Equilibrium conditions and equations of motion of a system in generalized coordinates

Index..........................