A Concise Introduction to Mechanics of Rigid Bodies: Multidisciplinary Engineering

1 Preliminary on vector, matrix, complex number and quaternion 1.1 Vector 1.1.1 Definition 1.1.2 Operations 1.2 Matrix 1.2.1 Definition 1.2.2 Operations 1.3 Complex number 1.3.1 Definition 1.3.2 Operations 1.4 Quaternion 1.4.1 Definition 1.4.2 Operations 1.4.3 Some definitions and relations 1.5 Special vectors, matrices and terms 2 Orientation and position representation 2.1 Coordinate frames 2.2 Observation frame, description frame and vector notations 2.3 Orientation 2.3.1 Rotation matrix 2.3.2 Equivalent/effective axis and angle 2.3.3 Exponential coordinates 2.3.4 Active / passive interpretations of rotation matrix and orientation from successive rotations 2.3.5 Euler angles 2.3.6 RPY angles 2.3.7 Quaternion of rotation 2.3.8 Cayley-Klein matrix 2.4 Position 2.4.1 Position of a rigid body and position of a point 2.4.2 Passive and active representation of position 2.5 Examples 3 Velocity and acceleration 3.1 Angular velocity 3.1.1 Angular velocity derived from rotation matrix 3.1.2 Angular velocity and the time derivative of a vector fixed in the body frame 3.1.3 Angular velocity derived from Euler angles and RPY angles 3.1.4 Angular velocity derived from equivalent/effective axis and angle 3.1.5 Angular velocity derived from quaternion of rotation 3.1.6 Angular velocity for successive rotations 3.2 Linear velocity 3.3 Acceleration 3.3.1 Angular acceleration 3.3.2 Linear acceleration 3.4 Examples 4 Dynamics 4.1 Inertial Properties 4.1.1 Inertial properties for linear motion 4.1.2 Inertial properties for angular motion 4.1.3 Inertia ellipsoid 4.1.4 Example 4.1.5 Theorems and rules 4.1.6 Examples 4.2 Momentum 4.2.1 Linear momentum 4.2.2 Angular momentum 4.2.3 Examples 4.3 Force, moment of force and torque 4.4 impulse, work and power 4.5 Mechanical energy 4.5.1 Kinetic energy 4.5.2 Potential energy 4.5.3 Mechanical energy 4.5.4 Examples 4.6 Equations of motion 4.6.1 Newton-Euler formulation 4.6.2 D'Alembert's principle 4.6.3 Lagrange's equations 4.6.4 Examples 5 Case studies 5.1 Two-link planar robotic arm 5.2 Human body doing twisting somersaults 5.3 Bicycle balance References Index