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1 Vectors for mechanics: position, force and moment
1.1Vector notation and vector addition
1.2The dot product of two vectors
1.4Moment and Moment about an Axis
1.5Solving vector equations
2 Free-Body Diagrams
2.1Equivalent force systems and couples
2.2Center of mass and center of gravity
2.4Contact forces: Sliding, rolling, and collisions
3 Computation: Algebra, ODEs, etc.
3.1Basic computation: linear equations and plotting
3.2ODEs, especially the common simple ODEs
5 Statics of one object
5.1Static equilibrium of a particle
5.2Static equilibrium of one body
5.3Equilibrium with frictional contact
6 Trusses and frames
6.2The method of sections
6.3Solving trusses on a computer
6.5Advanced truss analysis: determinacy, rigidity, and redundancy
7 Transmissions and mechanisms
7.2Levers, Wedges, Toggles, Gears and Pulleys
8 Tension, shear and bending moment
8.1Shear force, bending moment and tension diagrams
8.2Singularity functions: an algorithm for and diagrams
10 Dynamics in 1D
10.1Force and motion in 1D
10.3A mass and spring: the harmonic oscillator
10.4Coupled motions in 1D
11 Vibrations
11.2Forced Vibration and resonance
12 Particle dynamics in space (unconstrained)
12.1Dynamics of a particle in space
12.2Momentum and energy for particle motion
13 Two or more particles in space (unconstrained)
13.1Coupled motions of particles in space
13.2Collisions and explosions
14 Constrained straight-line motion
14.11D constrained motion and pulleys
14.21D motion with 2D and 3D forces
15 Circular motion of a particle
15.1Kinematics of a particle in circular motion
15.2Dynamics of a particle in circular motion
16 Circular motion of a rigid object
16.1Angular velocity of a rigid object
16.2Angular velocity of a rigid object
16.3Polar moment of inertia
16.4Dynamics of rigid-object planar circular motion
17 General planar motion of a single rigid object
17.1Rigid object kinematics
17.2Dynamics of a rigid object
17.3Kinematics of rolling and sliding
18 Kinematics using time-varying basis vectors
18.1Polar coordinates and path coordinates
18.2Rotating reference frames
18.3General expressions for velocity and acceleration
18.4Kinematics of 2-D mechanisms
18.5Advanced kinematics of planar motion
19 Mechanics of constrained particles and rigid objects
19.1Mechanics of a constrained particle
19.2One-degree-of-freedom 2-D mechanisms
19.3Multi-degree-of-freedom 2-D mechanisms
20 Fixed-axis rotation in 3D
20.13-D description of circular motion
20.2Dynamics of fixed axis rotation
20.3Moment of inertia matrices and
21 Elementary introduction to 3D rigid-object dynamics
21.1 and of points on a 3D rigid object
21.23D dynamics of a rigid body
Introduction to Mechanics for Engineers · © 2026 Andy Ruina and Rudra Pratap. All rights reserved.