Analytical Elements of Mechanics, Volume 2: Dynamics focuses on the processes, methodologies, approaches, and technologies involved in classical mechanics.
The book first offers information on the differentiation of vectors, including vector functions of a scalar variable; derivatives of sums and products; vector tangents of a space curve; vector binormals of a space curve; and Taylor's theorem for vector functions. The manuscript then ponders on kinematics, as well as angular velocity and acceleration, absolute and relative velocity and acceleration, and rates of change of orientation of a rigid body.
The text examines second moments and laws of motion. Discussions focus on second moments of sets of particles and continuous bodies, second moments of a point, motions of rigid bodies, and linear and angular momentum.
The publication is a dependable reference for readers interested in the dynamics of the analytical elements of mechanics.

Contenu

Preface
1 Differentiation Of Vectors
1.1 Vector Functions Of A Scalar Variable 1
1.1.1 Definition Of A Vector Function Of A Scalar Variable In A Reference Frame; Independence Of A Variable In A Reference Frame; Vectors Fixed In A Reference Frame
1.1.2 Dependence On A Variable In One Reference Frame, Independence Of The Same Variable In Another Reference Frame
1.1.3 Measure Numbers Characterize The Behavior Of A Vector Function
1.1.4 Constant Measure Numbers
1.1.5 Values Of A Vector Function
1.1.6 Equality
1.1.7 Dependence Of Results On The Reference Frame In Which An Operation Is Performed
1.1.8 Independence Of Results Of The Reference Frame In Which An Operation Is Performed
1.1.9 Notation
1.1.10 Expression Of Results In Terms Of Unit Vectors Fixed In Any Reference Frame
1.1.11 Functional Character Of Results Of Operations Involving Vector Functions
1.2 The First Derivative Of A Vector Function
1.2.1 Definition Of The First Derivative
1.2.2 First Derivatives Equal To Zero
1.2.3 Dimensions Of The First Derivative
1.2.4 Expression Of The First Derivative In Terms Of Unit Vectors Fixed In Any Reference Frame
1.2.5 Equality Of First Derivatives Of Equal Vector Functions
1.2.6 Notation
1.2.7 The First Derivative As A Limit
1.2.8 Properties Of The Derivative
1.3 The Second And Higher Derivatives Of Vector Functions 12
1.3.1 Definition Of The Second Derivative Of A Vector Function; Definition Of Higher Derivatives Of A Vector Function
1.4 Derivatives Of Sums
1.4.1 Equality Of The First Derivative Of A Sum And The Sum Of The First Derivatives
1.4.2 Applicability Of 1.4.1 To Second And Higher Derivatives
1.5 Derivatives Of Products
1.5.1 First Derivative Of The Product Of A Scalar And A Vector Function
1.5.2 First Derivative Of The Scalar Product Of Two Vectors
1.5.3 First Derivative Of The Vector Product Of Two Vectors
1.5.4 First Derivative Of The Continued Product Of Any Number Of Vector And Scalar Functions.
1.6 Derivatives Of Implicit Functions
1.6.1 First Derivative Of An Implicit Function Of A Scalar Variable
1.7 The First Derivative Of A Unit Vector Which Remains Perpendicular To A Line Fixed In A Reference Frame
1.7.1 Expression For The First Derivative
1.7.2 Interpretation Of One Of The Terms Appearing In 1.7.1, As A Rate Of Rotation.
1.7.3 Convenience Of 1.7.1 When Limited Information Available
1.8 Taylor's Theorem For Vector Functions
1.8.1 Statement Of The Theorem
1.8.2 The Use Of Taylor's Theorem For Purposes Of Computation And In Connection With Functions Not Specified Explicitly
1.9 Vector Tangents Of A Space Curve
1.9.1 Vector Tangents Expressed In Terms Of The First Derivative Of A Position Vector
1.9.2 Sense Of The Vector Tangents Obtained By Using Various Scalar Variables
1.9.3 Expression For The Vector Tangent In Terms Of The Derivative Of The Position Vector With Respect To Arc-Length Displacement
1.9.4 Definition Of The Normal Plane At A Point Of A Space Curve
1.10 Vector Binormals Of A Space Curve
1.10.1 Vector Binormals Expressed In Terms Of Derivatives Of A Position Vector
1.10.2 Perpendicularity Of Vector Tangents And Vector Binormals
1.10.3 Sense Of Vector Binormals Obtained By Using Various Scalar Variables
1.10.4 Simplification Introduced By The Use Of Arc-Length Displacement As Independent Variable
1.10.5 Definition Of The Plane Of Curvature Or Osculating Plane At A Point Of A Space Curve
1.11 The Vector Principal Normal Of A Space Curve
1.11.1 Definition Of The Vector Principal Normal
1.11.2 Expression For The Vector Principal Normal In Terms Of Derivatives Of A Position Vector
1.11.3 Expression For The Vector Principal Normal In Terms Of The Second Derivative With Respect To Arc-Length Displacement
1.11.4 Definition Of The Rectifying Plane At A Point Of A Space Curve
1.12 The Vector Radius Of Curvature Of A Space Curve
1.12.1 The Vector Radius Of Curvature Expressed In Terms Of Derivatives Of A Position Vector
1.12.2 The Vector Radius Of Curvature As The Product Of A Scalar And The Vector Principal Normal
1.12.3 Expressions In Terms Of Derivatives With Respect To Arc-Length Displacement
1.13 The Serret-Frenet Formulas
1.13.1 Derivatives Of Vector Tangents, Binormals, And Principal Normal With Respect To Arc-Length Displacement
1.13.2 The Torsion Of A Space Curve, Expressed In Terms Of Derivatives Of A Position Vector.
2.Kinematics
2.1 Rates Of Change Of Orientation Of A Rigid Body
2.1.1 Definition Of The Rate Of Change Of Orientation Of A Rigid Body In A Reference Frame With Respect To A Scalar Variable
2.1.2 Importance Of Rates Of Change Of Orientation As Analytical Tools
2.1.3 Symmetry Of The Expression For Rates Of Change Of Orientation
2.1.4 The Relationship Between The First Derivatives Of A Vector Function In Two Reference Frames
2.1.5 The Derivative In Two Reference Frames Of The Rate Of Change Of Orientation
2.1.6 Interchange Of Reference Frames
2.2 Angular Velocity
2.2.1 Definition Of The Angular Velocity Of A Rigid Body In A Reference Frame.
2.2.2 Expression For The Angular Velocity As A Product Of An Angular Speed Ancl A Unit Vector
2.2.3 Pictorial Representation Of Angular Velocity
2.2.4 Angular Velocity Of Fixed Orientation
2.2.5 Omission Of Qualifying Phrases In The Description Of Frequently Encountered Systems
2.2.6 Application Of 2.2.4 To The Motion Of Bodies Possessing No Fixed Point
2.2.7 Addition Of Angular Velocities
2.2.8 Resolution Of Angular Velocities Into Components
2.2.9 Kinematic Chains
2.2.10 Reference Frames Having No Physical Counterparts
2.3 Angular Acceleration
2.3.1 Definition Of The Angular Acceleration Of A Rigid Body In A Reference Frame
2.3.2 The Relationship Between Measure Numbers Of Components Of Angular Velocity And Angular Acceleration Vectors
2.3.3 Interchange Of Reference Frames
2.3.4 Expression For The Angular Acceleration As The Product Of A Scalar Angular Acceleration And A Unit Vector
2.3.5 The Relationship Between Angular Speed And Scalar Angular Acceleration
2.3.6 Pictorial Representation Of Angular Acceleration
2.3.7 Angular Acceleration Of A Body Having An Angular Velocity Of Fixed Orientation
2.3.8 Plane Linkages
2.3.9 Graphical Method For The Determination Of The Scalar Product Of Unit Vectors
2.3.10 Applicability Of 2.3.8 To Linkages Containing Sliding Pairs
2.3.11 Addition Of Angular Accelerations
2.4 Relative Velocity And Acceleration
2.4.1 Definitions Of Velocity And Acceleration Of One Point Relative To Another
2.4.2 The Relationship Between The Velocity Of P Relative To Q And The Velocity Of Q Relative To P
2.4.3 Relative Velocity And Acceleration Of Two Points Fixed In A Reference Frame
2.4.4 Addition O…