Newton-Euler Dynamics

Preface 1: Introduction and Basic Concepts 1.1 Fundamental Definitions and Assumptions1.2 Position, Velocity, and Acceleration of a Point2: Review of Planar Kinematics2.1 Plane Motion of a Point; Rectangular Components of Velocity and Acceleration 2.2 Example2.3 Tangential - Normal Components 2.4 Example2.5 Example2.6 Radial - Transverse Components 2.7 Example 2.8 Angular Velocity 2.9 Relative Motion of Reference Frames 2.10 Relative Velocity and Acceleration 2.11 Example 2.12 Example Notes Problems3: Coordinate Systems, Components, and Transformation 3.1 Rectangular Coordinates and Components 3.2 Intrinsic Components 3.3 Example 3.4 General Approach to Coordinate Systems and Components 3.5 Cylindrical Coordinates and Components 3.6 Example 3.7 Spherical Coordinates and Components 3.8 Coordinate Transformations 3.9 Examples Notes Problems4: Relative Motion 4.1 Introductory Remarks 4.2 Euler’s Theorem 4.3 Finite Rotations 4.4 Infinitesimal Rotations and Angular Velocity and Acceleration 4.5 Example 4.6 Basic Kinematic Equation 4.7 Some Properties of Angular Velocity 4.8 Relative Velocity and Acceleration Equations 4.9 Composition Relations for Angular Velocities and Accelerations 4.10 Summary of Relative Motion 4.11 Example Notes Problems 5: Foundations of Kinetics 5.1 Newton’s Laws of Motion 5.2 Center of Mass 5.3 Example 5.4 Rigid Bodies 5.5 Example 5.6 Example 5.7 Rigid Body Motion5.8 Proof That the Motion of a Rigid Body Is Specified By the Motion of Any Body-Fixed Frame 5.9 Proof That All Body-Fixed Frames Have the Same Angular Velocity 5.10 Gravitation5.11 Degrees of Freedom and Holonomic ConstraintsNotes Problems 6: Kinetics of the Mass Center of a Rigid Body 6.1Equations of Motion, Two Dimensions 6.2 Example 6.3 Aircraft Equations of Motion in a Vertical Plane 6.4 Equations of Motion, Three Dimensions 6.5 Example 6.6 Motion in Inertial and Non-Inertial Frames 6.7 Example - Rotating Cylindrical Space Station 6.8 Inertial Frames of Reference6.9 Motion Near the Surface of the Earth 6.10 Projectile Motion6.11 Example - Large Scale Weather Patterns 6.12 Aircraft Equations of Motion for 3-D Flight Notes Problems7: Angular Momentum and Inertia Matrix 7.1 Definition of Angular Momentum 7.2 Moments and Products of Inertia 7.3 Examples 7.4 Principal Axes and Principal Moments of Inertia 7.5 Example 7.6 Rotational Mass Symmetry 7.7 Relation Between Angular Momenta 7.8 Parallel Axis Theorem 7.9 Radius of Gyration 7.10 Examples Notes Problems8: Angular Momentum Equations 8.1 Angular Momentum Equation 8.2 Euler’s Equations 8.3 Summary of Rigid Body Motion 8.4 Examples 8.5 Special Case of Planar Motion 8.6 Example 8.7 Equivalent Force Systems Notes Problems9. Fixed Axis Rotation 9.1 Introductory Remarks 9.2 Off-Center Disk 9.3 Bent Disk 9.4 Static and Dynamic Balancing 9.5 General Case Notes Problems10: Motion of a Rigid Body with One Point Fixed; Gyroscopic Motion 10.1 Instantaneous Axis of Zero Velocity 10.2 Euler’s Angles 10.3 Transformations 10.4 Example - Thin Spherical Pendulum 10.5 Gyroscopic Motion 10.6 Steady Precession 10.7 Example 10.8 Steady Precession with Zero Moment 10.9 Steady Precession About an Axis Normal to the Spin Axis10.10 Use of a Rotor to Stabilize a Car in Turns 10.11 Examples and Applications Notes Problems11: Work and Energy 11.1 Introduction 11.2 Work 11.3 Forms of the Work Integral 11.4 Example - Constant Force 11.5 Power 11.6