Intermediate dynamics for engineers: Newton-Euler and Lagrandian mechanics

Contents
Preface
Part I A Single Particle
	1 Kinematics of a Particle
		1.1 Introduction
		1.2 Reference Frames
		1.3 Kinematics of a Particle
		1.4 Cartesian, Cylindrical Polar, and Spherical Polar Coordinate Systems
		1.5 Curvilinear Coordinates
		1.6 Examples of Curvilinear Coordinate Systems
		1.7 Representations of Particle Kinematics
		1.8 Kinetic Energy and Coordinate Singularities
		1.9 Constraints
		1.10 Classification of Constraints
		1.11 Closing Comments
		1.12 Exercises
	2 Kinetics of a Particle
		2.1 Introduction
		2.2 The Balance Law for a Single Particle
		2.3 Work and Power
		2.4 Conservative Forces
		2.5 Examples of Conservative Forces
		2.6 Constraint Forces
		2.7 Conservations
		2.8 Dynamics of a Particle in a Gravitational Field
		2.9 Dynamics of a Particle on a Spinning Cone
		2.10 A Shocking Constraint
		2.11 A Simple Model for a Roller Coaster
		2.12 Closing Comments
		2.13 Exercises
	3 Lagrange’s Equations of Motion for a Single Particle
		3.1 Introduction
		3.2 Lagrange’s Equations of Motion
		3.3 Equations of Motion for an Unconstrained Particle
		3.4 Lagrange’s Equations in the Presence of Constraints
		3.5 A Particle in Motion on a Smooth Surface of Revolution
		3.6 A Particle in Motion on a Sphere
		3.7 Some Elements of Geometry and Particle Kinematics
		3.8 The Geometry of Lagrange’s Equations of Motion
		3.9 Lagrange’s Equations of Motion for a Particle in the Presence of Friction
		3.10 A Particle in Motion on a Helix
		3.11 A Particle in Motion on a Moving Curve
		3.12 Closing Comments
		3.13 Exercises
Part II A System of Particles
	4 Lagrange’s Equations of Motion for a System of Particles
		4.1 Introduction
		4.2 A System of N Particles
		4.3 Coordinates
		4.4 Constraints and Constraint Forces
		4.5 Conservative Forces and Potential Energies
		4.6 Lagrange’s Equations of Motion
		4.7 Construction and Use of a Single Representative Particle
		4.8 Kinetic Energy, Mass Matrix, and Coordinate Singularities
		4.9 The Lagrangian
		4.10 A Constrained System of Particles
		4.11 A Canonical Form of Lagrange’s Equations
		4.12 Alternative Principles of Mechanics
			4.12.1 Principle of Virtual Work and D’Alembert’s Principle
			4.12.2 Gauss’ Principle of Least Constraint
			4.12.3 Hamilton’s Principle
		4.13 Closing Comments
		4.14 Exercises
	5 Dynamics of Systems of Particles
		5.1 Introduction
		5.2 Harmonic Oscillators
		5.3 A Dumbbell Satellite
		5.4 A Pendulum and a Cart
		5.5 Two Particles Tethered by an Inextensible String
		5.6 Closing Comments
		5.7 Exercises
Part III A Single Rigid Body
	6 Rotations and their Representations
		6.1 Introduction
		6.2 The Simplest Rotation
		6.3 Proper Orthogonal Tensors
		6.4 Derivatives of a Proper Orthogonal Tensor
		6.5 Euler’s Representation of a Rotation Tensor
		6.6 Euler’s Theorem: Rotation Tensors and Proper Orthogonal Tensors
		6.7 Relative Angular Velocity Vectors
		6.8 Euler Angles
			6.8.1 3–2–1 Euler Angles
			6.8.2 3–1–3 Euler Angles
			6.8.3 The Other Sets of Euler Angles
			6.8.4 Application to Joint Coordinate Systems
			6.8.5 Comments on Products of Rotations
		6.9 Further Representations of a Rotation Tensor
		6.10 Rotations, Quotient Spaces, and Projective Spaces
		6.11 Derivatives of Scalar Functions of Rotation Tensors
		6.12 Exercises
	7 Kinematics of Rigid Bodies
		7.1 Introduction
		7.2 The Motion of a Rigid Body
		7.3 The Angular Velocity and Angular Acceleration Vectors
		7.4 A Corotational Basis
		7.5 Three Distinct Axes of Rotation
		7.6 The Center of Mass and Linear Momentum
		7.7 Angular Momenta
		7.8 Euler Tensors and Inertia Tensors
		7.9 Angular Momentum and an Inertia Tensor
		7.10 Kinetic Energy
		7.11 Attitudes of Constant Angular Velocities
		7.12 Closing Comments
		7.13 Exercises
	8 Constraints on and Potential Energies for a Rigid Body
		8.1 Introduction
		8.2 Forces and Moments Acting on a Rigid Body
		8.3 Examples of Constrained Rigid Bodies
		8.4 Constraints and Lagrange’s Prescription
		8.5 Integrability Criteria
		8.6 Potential Energies, Conservative Forces, and Conservative Moments
		8.7 Closing Comments
		8.8 Exercises
	9 Kinetics of a Rigid Body
		9.1 Introduction
		9.2 Balance Laws for a Rigid Body
		9.3 Work and Energy Conservation
		9.4 Additional Forms of the Balance of Angular Momentum
		9.5 Moment-Free Motion of a Rigid Body
		9.6 The Baseball and the Football
		9.7 Motion of a Rigid Body with a Fixed Point
		9.8 Motions of Rolling Spheres and Sliding Spheres
		9.9 Chaplygin’s Sphere
		9.10 Closing Comments
		9.11 Exercises
	10 Lagrange’s Equations of Motion for a Single Rigid Body
		10.1 Introduction
		10.2 The Lagrange Top
		10.3 Configuration Manifold of an Unconstrained Rigid Body
		10.4 Lagrange’s Equations of Motion: A First Form
			10.4.1 Proof of Lagrange’s Equations
			10.4.2 The Four Identities
		10.5 A Satellite Problem
		10.6 Lagrange’s Equations of Motion: A Second Form
			10.6.1 Summary
		10.7 Lagrange’s Equations of Motion: Approach II
		10.8 Rolling Disks and Sliding Disks
		10.9 Lagrange and Poisson Tops
		10.10 Closing Comments
		10.11 Exercises
Part IV Systems of Particles and Rigid Bodies
	11 The Dynamics of Systems of Particles and Rigid Bodies
		11.1 Introduction
		11.2 Preliminaries
		11.3 A Planar Double Pendulum
		11.4 A Particle on a Rotating Circular Hoop
		11.5 Constraints
		11.6 A Canonical Function
		11.7 Integrability Criteria
		11.8 Constraint Forces and Constraint Moments
		11.9 Potential Energies, Conservative Forces, and Conservative Moments
		11.10 Lagrange’s Equations of Motion
		11.11 Two Pin-Jointed Rigid Bodies
		11.12 A Simple Model for a Spherical Robot
		11.13 A Semicircular Cylinder Rolling on a Cart
		11.14 A Single-Axis Rate Gyroscope
		11.15 Orthogonality of Generalized Forces and Gimbal Lock
		11.16 Closing Comments
		11.17 Exercises
Appendix A Background on Tensors
	A.1 Introduction
	A.2 Preliminaries: Bases, Alternators, and Kronecker Deltas
	A.3 The Tensor Product of Two Vectors
	A.4 Second-Order Tensors
	A.5 A Representation Theorem for Second-Order Tensors
	A.6 Functions of Second-Order Tensors
	A.7 Third-Order Tensors
	A.8 Special Types of Second-Order Tensors
	A.9 Derivatives of Tensors
	A.10 Exercises
References
Index