Contents of "Mechanics of Rigid Bodies"

 

 

Preface



 

PART I MATHEMATICAL BASICS

 

CHAPTER  1  VECTOR SPACE R3
- 1.1 Definition of the Vector Space R3
- 1.1.1 Vectors
- 1.1.2 Addition of Vectors
- 1.1.3 Multiplication by a Scalar
- 1.2 Linear Dependence and Independence. Basis of R3
- 1.2.1 Linear Combination
- 1.2.2 Linear Dependence and Independence
- 1.2.3 Basis for the Vector Space R3
- 1.2.4 Vector Components
- 1.3 Scalar Product of Two Vectors
- 1.3.1 Definition
- 1.3.2 Vector Norm
- 1.3.3 Analytical Expression for the Scalar Product in an Arbitrary Basis
- 1.3.4 Orthogonal Vectors
- 1.3.5 Orthonormal Basis
- 1.3.6 Expression for the Scalar Product in an Orthonormal Basis 
- 1.4 Vector Product
- 1.4.1 Definition 
- 1.4.2 Analytical Expression for the Vector Product in an Arbitrary Basis
- 1.4.3 Direct Basis
- 1.4.4 Expression for the Vector Product in a Direct Basis
- 1.4.5 Mixed Product of Three Vectors
- 1.4.6 Double Vector Product
- 1.5 Bases of the Vector Space R3
- 1.5.1 Canonical Basis
- 1.5.2 Change of Basis
-  Exercises
-  Comments

 

CHAPTER  2  THE GEOMETRIC SPACE
- 2.1 The Geometric Space Considered as Affine Space of the Vector Space R3
- 2.1.1  The Geometric Space
- 2.1.2 Consequences
- 2.1.3 Distance between two points
- 2.1.4 Angle between two bipoints
- 2.1.5 Reference Systems
- 2.2 Subspaces of the Geometric Space: Line, Plane
- 2.2.1 Line
- 2.2.2 Plane
- 2.2.3 Lines and Planes of Same Directions
- 2.2.4 Orthogonal Lines and Planes
- 2.3 Situating a Point of the Geometric Space
- 2.3.1 Coordinate Axes
- 2.3.2 Right-hand Orthonormal Frame
- 2.3.3 Cartesian Coordinates
- 2.4 The Equations of Plane and Line
- 2.4.1 Cartesian Equation of Plane
- 2.4.2 Cartesian Equation of Line
- 2.5 Change of Coordinate System
- 2.5.1 General Case
- 2.5.2 Systems with a Common Axis
- 2.5.3 Arbitrary Systems with a Common Origin. Eulerian Angles
-  Exercices
-  Comments

 

CHAPITER  3  VECTOR FUNCTION. DERIVATIVES
- 3.1 Vector Function of One Scalar Variable
- 3.1.1 Definition
- 3.1.2 Derivative
- 3.1.3 Propertis of the Vector Derivatives
- 3.1.4 Examples
- 3.2 Vector Function of Two Scalar Variables
- 3.2.1 Definition
- 3.2.2 Partial Derivatives
- 3.2.3 Examples
- 3.3 Vector Function of n Scalar Variables
- 3.3.1 Definitions
- 3.3.2 Examples
-  Commens

 

CHAPTER  4  ELEMENTS ON THE CURVES
- 4.1 Introduction
- 4.2 Curvilinear Abscissa. Length of Curve Arc
- 4.3 Tangent. Normal. Curvature Radius
- 4.4 Frenet Trihedron
-  Exercises
-  Comments

 

CHAPTER  5  TORSORS
- 5.1 Definition and Properties of Torsors
- 5.1.1 Definitions and Notations
- 5.1.2 Properties of Moment-Vectors
- 5.1.3 Vector Space of Torsors
- 5.1.4 Invariant Scalar of a Torsor 
- 5.1.5 Product of Two Torsors
- 5.1.6 Moment of a Torsor About a Given Axis
- 5.1.7 Central Axis of a Torsor
- 5.2 Particular Torsors. Resolution of an Arbitrary Torsor
- 5.2.1 Sliding-Torsor
- 5.2.2 Couple-Torsor
- 5.2.3 Arbitrary Torsor
- 5.2.4 Conclusions
- 5.3 Torsors associated to a Field of Sliding-Torsors defined on a Domain of the 

        Geometric Space
- 5.3.1 Torsor associated to a Discret Domain of Points
- 5.3.2 Torsor associated to a Continuous Domain
- 5.3.3 Imporatnt Particular Case. Measure Center.
-  Exercises
-  Comments

 

PART II  KINEMATICS

 

CHAPTER  6 KINEMATICS OF POINT
- 6.1 Introduction
- 6.2 Trajectory and Kinematic
- 6.2.1 Trajectory
- 6.2.2 Kinematic Vectors
- 6.2.3 Tangential and Normal Components of Kinematic Vectors
- 6.2.4 Different Types of Motions
- 6.3 Expressions of the Components of the Kinematic Vectors
- 6.3.1 Cartesian Coordinates
- 6.3.2 Cylindrical Coordinates
-  Exercises 
-  Comments

 

CHAPITRE  7  ANALYSIS OF PARTICULAR MOTIONS
- 7.1 Rectilinear Motions
- 7.1.1 Generalities
- 7.1.2 Uniform Rectilinear Motion
- 7.1.3 Uniformly Varied Rectilinear Motion
- 7.1.4 Vibratory Rectilinear Motion
- 7.2 Circular Motions
- 7.2.1 General Equations
- 7.2.2 Uniform Circular Motion
- 7.2.3 Uniformly Varied Circular Motion
- 7.3 Motions with Constant Acceleration Vector
- 7.3.1 Genaral Equations
- 7.3.2 Analysis of the Case where the Trajectory is Rectilinear
- 7.3.3 Analysis of the Case where the Trajectory is parabolic
- 7.4 Circular Helix Motion
- 7.5 Cycloidal Motion
-  Exercises
-  Comments

 

CHAPTER  8 MOTION WITH A CENTRAL ACCELERATION
- 8.1 General Properties
- 8.1.1 Definition
- 8.1.2 Motion with Central Acceleration is a plane Motion
- 8.1.3 Areal Velocity
- 8.1.4 Areal Law
- 8.1.5 Expressions of Kinematic Vectors
- 8.1.6 Polar Equation of the Trajectory
- 8.1.7 Motions for which the Acceleration is proportional to Position Vector
- 8.2 Central Acceleration Motions for which the accelaration is …….
- 8.2.1 Equations of the Trajectories
- 8.2.2 Analysis of the Trajectories
- 8.2.3 Magnitude of the Velocity Vector at a Point of the Trajectory
- 8.2.4 Elliptic Motion. Kepler’s Laws
-  Comments

 

CHAPTER  9 KINEMATICS OF RIGID BODY
- 9.1 Generalities
- 9.1.1 Notion of Rigid Body
- 9.1.2 Situating a Rigid Body
- 9.2 Relations between the Trajectories and the Kinematic Vectors  of Two Points

        attached to a Rigid Body
- 9.2.1 Relation between the Trajectories
- 9.2.2 Relation between the Velocity Vectors
- 9.2.3 Expression of the Instantaneous Angular Velocity Vector
- 9.2.4 Kinematic Torsor
- 9.2.5 Relation between the Acceleration Vectors
- 9.3 Generalizing the Composition of Motions 
- 9.3.1 Composition of Kinematic Torsors
- 9.3.2 Inverse Motions
- 9.4 Examples of Motions of Rigid Body
- 9.4.1 Rotation About a Fixed Axis
- 9.4.2 Translation of a Rigid Body
- 9.4.3 Motion of a Rigid Body with Hinge Connection
- 9.4.4 Motion of a Rigid Body About a Fixed Point
- 9.4.5 Plane Motion
-  Exercises
-  Comments

 

CHAPTER  10 KINEMATICS OF RIGID BODIES IN CONTACT
- 10.1 Kinematics of Two Rigid Bodies in Contact
- 10.1.1 Rigid Bodies in Contact at a Point. Sliding
- 10.1.2 Rotating and Rolling
- 10.1.3 Conclusions
- 10.1.4 Rigid Bodies in Contact at Several Points
- 10.2 Transmission of Rotation Motion
- 10.2.1 Generalities
- 10.2.2 Transmission by Friction
- 10.2.3 Gear Transmission
- 10.2.4 Belt Transmission
-  Exercises
-  Comments

 

PART III THE MECHANICAL ACTIONS

 

CHAPITRE  11 GENERAL CONCEPTS ON THE MECHANICAL ACTIONS
- 11.1 Basic Concepts Relative to Mechanical Actions
- 11.1.1 Notion of Mechanical Action
- 11.1.2 Representation of a Mechanical Action
- 11.1.3 Classification of Mechanical Actions
- 11.1.4 Mechanical Actions Exerted between Body Systems
- 11.1.5 Mechanical Actions Exerted on a System of Rigid Bodies
- 11.2 Different Types of Mechanical Actions
- 11.2.1 The Physical Natures of Mechanical Actions
- 11.2.2 Environment and Efficient Actions
- 11.3 Power and Work
- 11.3.1 Definition of Power
- 11.3.2 Change of Reference System
- 11.3.3 Potential Energy
- 11.3.4 Work
- 11.3.5 Power Developed by a Force
- 11.3.6 System of Rigid Bodies
-  Exercises
-  Comments

 

CHAPTER  12 GRAVITATION. GAVITY. MASS CENTER
- 12.1 Process of Gravitation
- 12.1.1 Law of Gravitation
- 12.1.2 Gravitational Field
- 12.1.3 Action of Gravitation Exerted by a Solid Sphere
- 12.1.4 Action of Gravitation Exerted by the Earth 
- 12.2 Action of Gravity 
- 12.2.1 Gravity Field
- 12.2.2 Action of Gravity exerted on a Body System
- 12.2.3 Power Developed by the Gravity Action
- 12.3 Determination of Mass Center
- 12.3.1 Mass Center of a System of Bodies
- 12.3.2 Mass Center of the Union of Two Systems
- 12.3.3 Mass Center of a Homogeneous Body
- 12.3.4 Homogeneous Bodies with Geometrical Symmetries
- 12.4 Examples of Determination of Mass Center
- 12.4.1 Solkid Hemisphere
- 12.4.2 Homogeneous Solid with Complex Geometry
- 12.4.3 Nonhomogeneous Solid
-  Exercises
-  Comments

 

CHAPTER  13 ACTIONS OF CONNECTIONS BETWEEN BODIES. CONNECTIONS
- 13.1 The Laws of Dry Friction between Rigid Bodies
- 13.1.1 Introduction
- 13.1.2 Contact at a Point
- 13.1.3 Couples of Resistance to Rolling and Rotating
- 13.2 Connections between Bodies
- 13.2.1 Introduction
- 13.2.2 Classification of Connections
- 13.2.3 Connection Action
- 13.2.4 Connection without Friction
- 13.2.5 Connection with Friction
-  Comments

 

CHAPITRE  14 STATICS OF RIGID BODIES
- 14.1 Introduction
- 14.2 Law of Statics
- 14.2.1 Case of a Rigid Body
- 14.2.2 Case of a System of Rigid Bodies
- 14.2.3 Mutual Actions
- 14.3 Statics of Wires or Flexible Cables
- 14.3.1 Mechanical Action Exerted by a Wire or a Flexible Cable
- 14.3.2 Equation of the Statics of a Wire
- 14.3.3 Wire or Flexible Cable subjected to Gravity Action
- 14.3.4 Contact of a Wire with a Rigid Body
- 14.4 Examples of Equilibrium
- 14.4.1 Case of a Rigid Body
- 14.4.2 Case of a System of Rigid Bodies
-  Exercises
-  Comments

 

PART IV KINETICS OF RIGID BODIES

 

CHAPITRE  15 THE OPERATOR OF INERTIA
- 15.1 Introduction to the Operator of Inertia
- 15.1.1 Operator Associated to the Vector Produc 
- 15.1.2 Extension of the Previous Result
- 15.1.3 The Operator of Inertia
- 15.2 Change of Reference System
- 15.2.1 Change of the Origin
- 15.2.2 Huyghens’s Relations
- 15.2.3 Diagonalization of the Inertia Matrix
- 15.2.4 Change of Basis
- 15.3 Moments of Inertia with respect to a Point, an Axis or a Plane
- 15.3.1 Definitions
- 15.3.2 Relations between the Moments of Inertia
- 15.3.3 Case of a Plane Body 
- 15.3.4 Moment of Inertia with respect to an Arbitrary Axis 
- 15.4 Determination of Matrices of Inertia
- 15.4.1 Bodies with Material Symmetries
- 15.4.2 Body with Cylindrical Symmetry
- 15.4.3 Body with Spherical Symmetry
- 15.4.4 Associativity
- 15.5 Matrices of Inertia of Usual Homogeneous Bodies
- 15.5.1 One-Dimensional Bodies
- 15.5.2 Two-Dimensional Bodies
- 15.5.3 Three-Dimensional Bodies
-  Exercises
-  Comments

 

CHAPTER  16  KINETIC TORSOR. DYNAMIC TORSOR. KINETIC ENERGY
- 16.1 Kinetic Torsor
- 16.1.1 Definition
- 16.1.2 Kinetic Torsor Associated with the Motion of a Rigid Body
- 16.1.3 Kinetic Torsor Associated with a System of Rigid Bodies
- 16.2 Dynamic Torsor
- 16.2.1 Definition
- 16.2.2 Dynamic Torsor Associated with the Motion of a Rigid Body
- 16.2.3 Dynamic Torsor Associated with a System of Rigid Bodies
- 16.2.4 Relation with the Kinetic Torsor
- 16.3 Kinetic Energy
- 16.3.1 Definition
- 16.3.2  Kinetic Energy of Rigid Body
- 16.3.3  Kinetic Energy of a System of Rigid Bodies
- 16.3.4  Derivative of the Kinetic Energy of a Body with respect to Time
-  Exercises
-  Comments

 

CHAPTER  17 CHANGE OF REFERENCE SYSTEM
- 17.1 Kinematics of the Change of Reference System
- 17.1.1 Relation between the Kinematic Torsors
- 17.1.2 Relation between Velocity Vectors. Training Velocity
- 17.1.3 Composition of Acceleration Vectors
- 17.2 Dynamic Torsors
- 17.2.1 Torsor of Training Inertia
- 17.2.2 Torsor of Coriolis Inertia
- 17.2.3 Relation between the Dynamic Torsors Evaluated in Two Different Reference Systems
-  Comments

 

PARTIE V DYNAMICS OF RIGID BODIES

 

CHAPTYER  18  THE FUNDAMENTAL PRINCIPLE OF THE DYNAMICS AND ITS

                       CONSEQUENCES
- 18.1 The Fundamental Principle
- 18.1.1 Statement of the Fundamental Principle of Dynamics
- 18.1.2 Class of Galilean Reference Systems
- 18.1.3 Vector Equations Deduced from Fundamental Principle
- 18.1.4 Scalar Equations Deduced from Fundamental Principle
- 18.2 Mutual Actions
- 18.2.1 Theorems of Mutual Actions
- 18.2.2 Transmission of Mechanical Actions
- 18.3 Theorem of Energy-Power
- 18.3.1 Case of a Rigid Body
- 18.3.2 Case of a System of Rigid Bodies
- 18.3.3 Mechanical Actions with Potential Energy
- 18.4 Application of the Fundamental Principle to the Analysis of the Motion of a Rigid

          Body Free in a Galilean Reference System
- 18.4.1 The General Problem
- 18.4.2 Particular Cases
- 18.5 Application to the Sun System
- 18.5.1 Galilean Reference System
- 18.5.2 Motion of the Planets
- 18.5.3 The Earth in the Sun System
-  Comments

 

CHAPTER  19  THE FUNBDAMENTAL EQUATION IN THE DIFFERENCE REFERENCE

                     SYSTEMS
- 19.1 Generalities
- 19.1.1 The Fundamental Equation of the Dynamics in a Non Galilean System
- 19.1.2 The Different Reference Systems Used in Mechanics
- 19.2 The Fundamental Equation of the Dynamics in the Geocentric Reference System
- 19.2.1 General Equations
- 19.2.2 Rigid Body Located in the Vicinity of the Earth
- 19.3 The Fundamental Equation of the Dynamics in a Reference System Attached to

          the Earth
- 19.3.1 General Equations
- 19.3.2 Action of Gravity
- 19.3.3 Conclusions on the Equations of the Dynamics with respect to a Refernce

            System Attached to the Earth
- 19.4 Equations of the Dynamics of a Body with respect to a Reference System

          whose Motion is Given Relatively to the Earth
- Comments

 

CHAPTER  20 GENERALITIES ON THE DYNAMICS OF A RIGID BODY OR ASYTEM OF

                    RIGID BODIES
- 20.1 Dynamics of a Rigid Body
- 20.1.1 General Equations
- 20.1.2 Process of General Analysis
- 20.2 Dynamics of a System of Rigid Bodies
- 20.3 Conclusions
- Comments

 

CHAPTER  21  DYNAMICS OF A SYSTEM WITH ONE DEGREE OF FREEDOM. ANALYSIS

                     OF VIBRATIONS 
- 21.1 General Equations
- 21.1.1 Introduction
- 21.1.2 Parameters of Situation
- 21.1.3 Kinematics
- 21.1.4 Kinetics
- 21.1.5 Mechanical Actions Exerted on the System
- 21.1.6 Application of the Fundamental Principle
- 21.2 Vibrations without Friction
- 21.2.1 Equation of Motion
- 21.2.2 Free Vibrations
- 21.2.3 Forced Vibrations. Steady State
- 21.3 Vibrations with Viscous Friction
- 21.3.1 Equation of Motion
- 21.3.2 Free Vibrations
- 21.3.3 Harmonic Forced Vibrations
- 21.3.4 Forced Vibrations in the case of a Periodic Imposed Force
- 21.3.5 Forced Vibrations in the case of an Arbitrary Imposed Force
- 21.3.6 Forced Vibrations in the case of a Motion Imposed to Support
- 21.4 Vibrations with Dry Friction
- 21.4.1 Equations of Motion
- 21.4.2 Free Vibrations
- 21.5 Equivalent Viscous Damping
- 21.5.1 Introduction
- 21.5.2 Work of the Force and Energy Dissipated in the case of Viscous Damping
- 21.5.3 Structural Damping
- 21.5.4 Dry Friction
- 21.5.5 Fluid Damping
- 21.5.6 Conclusion
-  Exercices
-  Commentaires

 

CHAPTER  22 ROTATION OF A RIGID BODY ABOUT A FIXED AXIS
- 22.1 General Equations
- 22.1.1 Introduction
- 22.1.2 Parameters of Situation
- 22.1.3 Kinematics
- 22.1.4 Kinetics
- 22.1.5 Mechanical Actions mécaniques Exerted on the Body
- 22.1.6 Application of the Fundamental Principle of Dynamics
- 22.2 Examples of Motions of Rotation about an Axis
- 22.2.1 Rigid Body in Rotation Subjected only to Gravity
- 22.2.2 Torsion Pendulum
- 22.3 The Problem of Balancing Rotating Bodies
- 22.3.1 General Equations of an Unbalanced Rotating Body
- 22.3.2 Mechanical Actions Exerted on the Axis of Rotor
- 22.3.3 Principle and Realisation of Balancing
-  Exercises
-  Comments

 

CHAPTER  23 PLANE MOTION OF A RIGID BODY
- 23.1 Introduction
- 23.2 Motion of a Parallelepiped on an Incline Plane
- 23.2.1 Parameters of Situation and Kinematics
- 23.2.2 Kinetics of the Motion
- 23.2.3 Mechanical Actions Exerted on the Parallelepiped
- 23.2.4 Equations Deduced from the Fundamental Principle
- 23.2.5 Motion without Friction
- 23.2.6 Motion with Dry Friction
- 23.2.7 Motion with Viscous Friction
- 23.3 Analysis of Sliding and Rocking of a Parallelepiped on an Incline Plane
- 23.3.1 Introduction
- 23.3.2 Parametrs of Situation and Kinematics
- 23.3.3 General Equations
- 23.3.4 Analysis of the Different Motions
- 23.3.5 Conclusions
- 23.4 Motion of a Cylinder on an Incline Plane
- 23.4.1 Introduction
- 23.4.2 Parameters of Situation and Kinematics
- 23.4.3 Mechanical Actions Exerted on the Cylinder
- 23.4.4 General Equations
- 23.4.5 Analysis of the Different Motions
- 23.5 Conclusions
-  Comments

 

CHAPTER  24 ANOTHER EXAMPLES OF MOTIONS OF RIGID BODIES
- 24.1 Translation Motion
- 24.1.1 General Equations
- 24.1.2 Free Body Submitted to Gravity
- 24.2 Motion of a Rigid Body Lying on a Wagon
- 24.2.1 Introduction
- 24.2.2 Parameters of Situation
- 24.2.3 Kinetics
- 24.2.4 Analysis of the Mechanical Actions
- 24.2.5 Equations of Dynamics
- 24.2.6 Analysis of the Different Motions
- 24.3 Coupled Motions of Two Rigid Bodies
- 24.3.1 Introduction
- 24.3.2 Parameters of Situation and Kinematics
- 24.3.3 Kinetics
- 24.3.4 Analysis of the Mechanical Actions
- 24.3.5 Equations Deduced from the Fundamental Principle
- 24.3.6 Equations of Motion
-  Exercises
-  Comments

 

CHAPTER  25 LAGRANGE’S EQUATIONS
- 25.1 GENERALITIES
- 25.1.1 Free Body and Connected Body
- 25.1.2 Partial Kinematics Torsors
- 25.1.3 Power Coefficients
- 25.1.4 Connections without Friction
- 25.2 Lagrange’s Equations Relative to the Motion of a Rigid Body
- 25.2.1 Introduction to Lagrange’s Equations
- 25.2.2 Lagrange’s Equations
- 25.2.3 Case where the Mechanical Actions are Derived from a Potential Energy
- 25.3 Lagrange’s Equations for a System of Rigid Bodies
- 25.3.1 Lagrange’s Equations for Each Body
- 25.3.2 Lagrange’s Equations for the System of Bodies
- 25.3.3 Case where the Parameters of Situation are Linked
- 25.4 Applications
- 25.4.1 Parallelepiped on an Incline Plane
- 25.4.2 Motion of Two Coupled Bodies
- 25.4.3 Double Pendulum
- A.25 Appendix
-  Exercises
-  Comments

PART VI  NUMERICAL METHODS FOR SOLVING THE EQUATIONS OF

                MOTIONS

 

CHAPTER  26 NUMERICAL SOLVING OF FIRST-ORDER DIFFERENTIAL EQUATIONS
- 26.1 Generalities
- 26.1.1 Problem Statement with Given Initial Conditions
- 26.1.2 General Method for Nulerical Solving
- 26.1.3 The Euler’s Method
- 26.2 One-Step Procedures
- 26.2.1 General Features
- 26.2.2 Procedures of Runge-Kutta Type
- 26.2.3 Romberg’s Methods
- 26.3 Multiple-Step Procedures
- 26.3.1 Introduction to Multiple-Steps Methods
- 26.3.2 Methods Based on the Newton’s Interpolation
- 26.3.3 Generalization of the Multiple-Step Methods
- 26.3.4 Examples of Multiple-Step Methods
- 26.3.5 Results
-  Exercises
-  Comments

 

CHAPTER  27 NUMERICAL PROCEDURES FOR SOLVING THE EQUATIONS OF MOTIONS
- 27.1 Equation of Motion of a Body with One Degree of Freedom
- 27.1.1 Form of the Equation of Motion with One Degree of Freedom
- 27.1.2 Principle of the Numerical Solving
- 27.1.3 Application to he Motion of Pendulum
- 27.2 Equations of Motion with Multiple Degrees of Freedom
- 27.2.1 Form of Equations of Motion with Multiple Degrees of Freedom
- 27.2.2 Principle of Solving
- 27.2.3 Trajectories and Kinematic Vectors
- 27.3 Planetary and Satellite Motions
- 27.3.1 Planetary Motion
- 27.3.2 Motion of Earth Satellite
- 27.3.3 Launching and Motion of a Moon Schuttle
- 27.4 Mootion with Viscous Friction of a Body on an Incline Plane
- 27.5 Motion of Two Coupled Solids
- 27.5.1 Equations of Motion
- 27.5.2 Analytical Solving in the case of Low Amplitudes of Vibrations and without

             Friction
- 27.5.3 Numerical Solving of Motion Equations

 

PART VII SOLUTIONS OF THE EXERCISES

 

- Chapter 1  Vector Space R3
- Chapter 2  The Geometric Space
- Chapter 4  Elements on the Curves
- Chapter 5  Torsors
- Chapter 6  Kinematics of Point
- Chapter 7  Analysis of Particular Motions
- Chapter 9  Kinematics of Rigid Body
- Chapter 10  Kinematics of Rigid Bodies in Contact
- Chapter 11  General Concepts on the Mechanical Actions
- Chapter 12  Gravitation. Gravity. Mass Center
- Chapter 14  Statics of Rigid Bodies
- Chapter 15  The Operator of Inertia
- Chapter 16  Kinetic Torsor. Dynamic Torsor. Kinetic Energy
- Chapter 21  Dynamics of a System with One Degree of Freedom. Analysis of Vibrations
- Chapter 22  Rotation of a Rigid Body about a Fixed Axis
- Chapter 24  Another Examples of Motions
- Chapter 25  Lagrange’s Equations