Ruina A., Pratap R. Introduction to Statics and Dynamics

Pre-print for Oxford University Press, 2002. 765 p.To the studentWhat is mechanics?Vectors for mechanics
Vector notation and vector addition
The dot product of two vectors
Cross product, moment, and moment about an axis
Solving vector equations
Equivalent force systemsFree body diagrams
Free body diagramsStatics
Static equilibrium of one body
Elementary truss analysis
Advanced truss analysis: determinacy, rigidity, and redundancy
Internal forces
Springs
Structures and machines
Hydrostatics
Advanced staticsDynamics of particles
Force and motion in 1D
Energy methods in 1D
The harmonic oscillator
More on vibrations: damping
Forced oscillations and resonance
Coupled motions in 1D
Time derivative of a vector: position, velocity and acceleration
Spatial dynamics of a particle
Central-force motion and celestial mechanics
Coupled motions of particles in spaceConstrained straight line motion
D constrained motion and pulleys
D and 3-D forces even though the motion is straightCircular motion
Kinematics of a particle in planar circular motion
Dynamics of a particle in circular motion
Kinematics of a rigid body in planar circular motion
Dynamics of a rigid body in planar circular motion
Polar moment of inertia: Izczm and IzOz
Using Izczm and IzOz in 2-D circular motion dynamicsGeneral planar motion of a single rigid body
Kinematics of planar rigid-body motion
General planar mechanics of a rigid-body
Kinematics of rolling and sliding
Mechanics of contacting bodies: rolling and sliding
CollisionsKinematics using time-varying base vectors
Polar coordinates and path coordinates
Rotating reference frames and their time-varying base vectors
General expressions for velocity and acceleration
Kinematics of 2-D mechanisms
Advance kinematics of planar motionMechanics of constrained particles and rigid bodies
Mechanics of a constrained particle and of a particle relative to a moving frame
Mechanics of one-degree-of-freedom 2-D mechanisms
Dynamics of rigid bodies in multi-degree-of-freedom 2-D mechanismsIntroduction to three dimensional rigid body mechanics
D description of circular motion
Dynamics of fixed-axis rotation
Moment of inertia matrices
Mechanics using the moment of inertia matrix
Dynamic balanceA Units and dimensions
Units and dimensions
B Contact: friction and collisions
Contact laws are all rough approximations
Friction
A short critique of Coulomb friction
Collision mechanics
Homework problems
Answers to *’d problems