• ### Chapter 1: Particle Kinematics

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1. Introduction
2. Reference Frame
3. Coordinate System
3.1 Cartesian Coordinate System
3.2 Cylindrical Coordinate System
3.3 Spherical Coordinate System
4. The Time Derivative of Vectors
5. Velocity and Acceleration Vector of a Particle
5.1 Definitions
5.2 Velocity & Acceleration in Cartesian Coordinates
Example: the sound of a cannonball
5.3 Velocity & Acceleration in Cylindrical Coordinates
Example: the three bug problem
5.4 Velocity & Acceleration in Spherical Coordinates
Example: the loxodrome
6. Special Motions
6.1 Uniform Motion
6.2 Motion at Constant Velocity
Example
6.3 Motion with Constant Acceleration
Example
6.4 Circular Motion
6.5 Motion with Central Acceleration
Example 1
Example 2
7. Intrinsic Coordinate System
Example 1: the radius of curvature of a planar curve
Example 2: the regular circular helix
Example 3: the design of highway interchange
Example 4: the radius of curvature of the loxodrome

Problems
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• Chapter 2: Rigid Body Kinematics - Part 1
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1. Introduction

2. Position of Referential  F relative to referential E
2.1 Assumptions: Notion of Absolute Time
2.2 Parametrization of  relative to
2.3 Euler Angles
2.4. Examples
Example 1
Example 2
Example 3
Example 4

3. Translational Motion

4. Rotational Motion

5. Kinematics of the General Motion of Referentia F  relative to
referential E
5.1. Angular Velocity Between Two Referentials
5.2 Practical Determination of Angular Velocities
5.3. Examples
Example 1: determination of the velocity of a particle in
spherical coordinates
Example 2: the angular velocity in terms of Euler angles
Example 3: a system of 2 articulated arms
Example 4: A gyroscopic system
Example 5
5.4. On the relationships between direction cosines and the angular
velocity
5.5. Angular Acceleration of  relative to
5.6. Velocity Field of  relative to
Example 1
Example 2

6. Screws
6.1 Definition
6.2 Operations of the Set of Screws: Equality and Sum of Two Screws
6.3 Properties of Screws
6.3.1 The invariants of a screw
6.3.2 Equiprojectivity
6.4 Two Elementary Classes of Screws: Couples and Sliders
6.4.1 Couples
6.4.2 Sliders
6.5 Is the sum of sliders a slider?
Problem 1
Problem 2
6.6 The Axis of a Screw
6.7 The scalar product of two screws
6.8 Another Class of Screws

7. The Kinematic Screw

7.1 Definition
7.2 Properties of the Kinematic Screw
Example 1

8. Acceleration Field of Referential  relative to Referential

9. Change of Referential
9.1. Notion of Coinciding Point
9.2. Change of Referential for Velocities
9.3. Change of Referential for Accelerations
9.4. Special Cases
9.4.1. Translation
9.4.2. Rotation
9.5. Examples
Example 1
Example 2
Example 3
Example 4

10. Addition Rule of Kinematic Screws

Problems

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• Chapter 3: Rigid Body Kinematics - Part 2
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1. Overview
2. Constraints between Rigid Bodies
2.1. Geometric versus Kinematic Constraints
2.2. Examples
Example 1: Sphere, Disk, and Cylinder Constrained to a Plane
Example 2: Rod Sliding on Wall
Example 3: Sliding Plate
Example 4: Rod inside Interior of Sphere

3. Examples of geometric constraints between two rigid bodies S1 and
S2: Kinematic Pairs
3.1 Slider
3.2 Pivot
3.3 Slider-Pivot
3.4 Screw
3.5 Spherical Joint
3.6 Planar Joint
3.7 Tubular Joint
3.8 Cylindrical Joint
3.9 Conical Joint

4. Kinematics of the Point Contact between Two Rigid Bodies
4.1. Generalities
4.2. The slip-velocity at I of S2  relative to S1
4.3. The pivoting and rolling of S2 relative to S1
4.4. The Fixed and Moving Axodes of a General Motion
4.5. Examples
Example 1: The Rolling Motion of a Cylindrical Tube
Example 2: The no-slip motion of a disk on a horizontal support
Example 3: The no-slip motion of a sphere on a spherical surface
Example 4: Two shafts in rolling contact
Example 5: Kinematic Analysis of Tapered Roller Bearings

5. Planar Kinematics
5.1. Definition of Planar Motion
5.2. Instantaneous center of rotation
5.3. The fixed and moving centrodes of the motion
5.4. Example: The planar motion of a rod
5.5. Three rigid bodies in planar motion: Kennedy's theorem
5.6. Examples
Example 1

6. Kinematical Analysis of Mechanisms
6.1. Example 1: Kinematic Analysis of a Computer Mouse
6.2. Example 2: the Universal Joint
6.3. Example 3: Automatic Gate Opening/Closing Mechanism

Problems

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• Chapter 4: Kinetics of Material Systems
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1. Overview
2. Material Systems: Definition
3. Mass Center of a Material System
4. A General Class of Screws
5. Kinetic Screw of Material System
5.1. Definition
5.2. Theorem of the Mass Center

6. Dynamic Screw of a Material System
7. Relationship between angular momentum and dynamic moment
8. Kinetic Energy of a Material System
9. The Calculation of Angular Momentum of a Rigid Body
10. Inertia Operator of a Rigid Body about a Point
10.1. Definition
10.2. Properties
10.3. Moment of inertia w.r.t. an axis
10.4. Parallel axis theorem
10.5. Inertia operators and material symmetries

11. Determination of the Angular Momentum of a Rigid Body
11.1. Assumptions and derivation
11.2. Particular cases

12. Determination of the Kinetic Energy of a Rigid Body
12.1. Assumptions and derivation
12.2 Particular cases

13. Examples
Example 1
Example 2
Example 3
Example 4
Example 5

Problems
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• Chapter 5: Particle Dynamics
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1. Overview
2. Newton's Laws
2.1. Newton's first law
2.2. Newton's second law
2.3. Newton's third law or principle of action and reaction

3. Newtonian Referentials
3.1. Class of Newtonian Referentials
3.2. Approximate Newtonian Referentials

4. Action-at-a-distance Forces
4.1. Gravitational Forces
4.1.1 Newton's Law of Gravitation
4.1.2 Gravitational Field due to a Celestial Body on a Particle
4.1.3 Gravitational Field of a Body with Spherical Symmetry
4.1.4 Weight of a Particle and Gravitational Acceleration

5. Contact Forces
5.1 Reaction forces of a Rigid Body on a Particle
5.1.1. Introduction
5.1.2. Frictionless Contact
5.1.3. Contact with Friction
5.1.4. Examples
5.2 Force exected by a string
5.3 Force exected by a spring
5.4 Force exected by a fluid

6. Linear Momentum, Angular Momentum of a Particle
6.1. Linear Momentum
6.2. Linear Momentum Form of Newton's Law
6.3. Angular Momentum, Moment of a Force
6.4. Angular Momentum Form of Newton's Second Law

7. Work, Power, Potential Energy
7.1. Power & Work
7.2. Potential of a Force Field
7.3. Work-Energy Principle
7.4. Conservation of Mechanical Energy

8. Motion of a Particle in a One-Dimensional Potential
8.1. Assumptions
8.2. Equilibrium Positions
8.3. Stability of an Equilibrium Point
8.4. Possible Motions
8.5. Application: Motion under a Conservative Central Force
8.6. Example

9. Extension of Newton's Second Law Relative to a Non-Newtonian
Referential
9.1. Newton's Law in a Non-Newtonian Referential
9.2. Use of a Terrestrial Referential
9.3. Foucault's Pendulum
9.4. Use of the Geocentric Referential
9.5. Examples
Example 1: the eastward (and southward) deviation of a
free-falling particle

Problems
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• Chapter 6: Dynamics of Systems of Particles
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1. Overview
2. Kinetics of a System of Particles
2.1 Linear and Angular Momenta: Kinetic Screw
2.2 Dynamic Screw
2.3 Relationship between the Kinetic and Dynamic Screws
2.4 Kinetics in the Centroidal Referential of a System

3. Forces Acting on a System: Action Screw
3.1. External/Internal Forces
3.2. External/Internal Moments
3.3. The Action Screw

4. Extension of Newton's Laws for a System of Particles
4.1 Extension of Newton's second law: the Fundamental Theorem of
Dynamics
4.2 Extension of Newton's third law
4.3 The Fundamental Theorem relative to the centroidal referential
of a system

5. Power, Kinetic Energy & Energy Theorems
5.1. Work & Power of External Forces
5.2. Work & Power of Internal Forces
5.3. Theorem of the Kinetic Energy
5.4. D'Alembert Principle of Virtual Power

6. Application: The Two-Body Problem
6.1. Isolated System of Two Particles
6.2. First Integrals of Motion
6.3. Reduced Problem
6.4. Case of Gravitational Attraction

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• Chapter 7: Rigid Body Dynamics
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1. Overview
2. The Modeling of the Mechanical Efforts on a Material System
2.1. Internal versus External Efforts
2.2. Action-at-a-Distance Efforts
2.3. Contact Actions
2.4. The External Action Screw exerted on a Material System

3. D'Alembert Generalized Principle of Virtual Power
3.1 Statement of the Principle
3.2 Corollary: action and reaction screws

4. The Fundamental Theorem of Dynamics
4.1. Derivation
4.2. Particular Cases

5. Contact Efforts Between Two Rigid Bodies: Coulomb Laws of Dry
Friction
5.1 Point-contact
5.1.1. Frictionless Contact between two Rigid Bodies
5.1.2. Coulomb Laws of Sliding Friction
5.1.3. Rolling and Spinning Friction
5.2. Rigid bodies in line- or surface-contact
5.3. Examples
5.3.1 Example 1
5.3.2 Example 2
5.3.3 Example 3
5.3.4 Example 4

6. Frictionless Joints between Two Rigid Bodies
6.1. Frictionless Pivot
6.2. Frictionless Slider
6.3 Frictionless Slider-Pivot
6.4 Frictionless Helical Joint or Screw
6.5 Frictionless Spherical Joint
6.6 Examples
Example 1
Example 2

7. Conservation Laws: First Integral of Motion
7.1 From Euler's first principle
7.2. From Euler's second principle

8. The Fundamental Theorem of Dynamics relative to a Non-Newtonian
Referentials
8.1. Statement
8.2. Example
8.3. Analytical Expressions of the Entrainement and Coriolis Inertia
Screws

9. Special Motions
9.1. Rigid Body in Rotation about a Fixed Axis
9.2. Euler-Poinsot Motion
9.2.1. Case 1
9.2.2. Case 2

10. Dynamic Balancing
11. Gyroscopic Effects
11.1 Definition
11.2. General Properties
11.3. Motion of a Top

Problems
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• Appendix