Theoretical and applied mechanics / / Valentin Molotnikov, Antonina Molotnikova

• Autore: Molotnikov Valentin
• Pubblicazione: Cham, Switzerland : , : Springer, , [2023]; ©2023
• Descrizione fisica: 1 online resource (687 pages)
• Disciplina: 531
• Soggetto topico: Mechanics
• Persona (resp. second.): MolotnikovaAntonina
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Intro -- Abstract -- Acknowledgements -- Introduction -- Contents -- Notation Conventions -- Theoretical Mechanics -- Theory of Mechanisms and Machines -- Resistance of Materials -- Machine Parts and Design Basics -- Introduction to CAD Based on AutoCad AutoLisp -- Part I Theoretical Mechanics -- 1 Statics -- 1.1 Introduction -- 1.2 The Subject and Tasks of Theoretical Mechanics -- 1.3 Strength. Force syste -- 1.4 Axioms of Theoretical Mechanics -- 1.5 Connections and Their Reactions -- 1.5.1 Classification of Constraints -- 1.6 Conditions for the Equilibrium of Converging Forces -- 1.7 A System of Parallel Forces: Power Pairs -- 1.8 Moment of Force Relative to the Point and Axis -- 1.9 Basic Theorem of Statics -- 1.10 Equilibrium of an Arbitrary System of Forces -- 1.11 Solving Problems on the Balance of Systems of Forces -- 1.11.1 General Comment -- 1.11.2 Example 1 -- 1.11.3 Example 2 -- 1.11.4 Example 3 -- 1.12 Truss Calculation -- 1.12.1 Calculation of a Triangular Cantilever Truss -- 1.12.2 Calculation of a Symmetrical Bridge Girder -- 1.13 Computer Calculation of Truss -- 1.14 Center of Parallel Forces -- 1.15 The Center of Gravity of a Rigid Body -- Self-Test Questions -- Self-Test Questions -- Control Tasks for the Section ``Statics'' -- Example of Completing a Task -- References -- 2 Kinematics -- 2.1 Ways to Set the Movement -- 2.2 Speed and Acceleration of the Point -- 2.3 The Simplest Movements of a Solid Body -- 2.3.1 Forward Motion of a Solid Body -- 2.3.2 Rotation of a Solid Body Around a Fixed Axis -- 2.4 Complicated Motion of a Point -- 2.5 Flat Solid Motion -- 2.5.1 Equations of Plane Motion of a Solid Body -- 2.5.2 Angular Velocity and Angular Acceleration in Plane Motion -- 2.5.3 Speed Points in Planar Movement of the Body -- 2.5.4 Instant Center of Velocity -- 2.5.5 Speed Plan. ; 2.5.6 Determination of Accelerations of Points of a Body in Flat Motion -- 2.6 Complex Motion of Points in the General Case -- 2.6.1 Absolute and Relative Derivatives of a Vector Function of a Scalar Argument -- 2.6.2 Addition of Velocities -- 2.6.3 Acceleration of a Point in the General Case of Portable Motion -- Self-Test Questions -- Self-Test Questions -- Control Tasks for the Section ``Kinematics'' -- Example of Completing a Task -- References -- 3 Dynamics -- 3.1 Point Dynamics -- 3.2 Dynamic Coriolis Theorem -- 3.3 General Theorems of Dynamics of a Point -- 3.3.1 Basic Concepts and Definitions -- 3.3.2 Theorem on Changing the Amount of Motion Material Point -- 3.3.3 Theorem on Changing the Kinetic Energy of a Point -- 3.3.4 Theorem on Changing the Moment of the Amount of Motion of a Point -- 3.4 System Dynamics -- 3.4.1 The Geometry of the Masses -- 3.4.2 Theorem on the Motion of the Center of Mass of the System -- 3.4.3 Theorem on Changing the Amount of Motion of a System -- 3.4.4 Theorem on Changing the Moment of Quantity of Motion of the System -- 3.4.5 Theorem on Changing the Kinetic Energy of aSystem -- 3.5 The d'Alembert Principle -- Self-Test Questions -- Self-Test Questions -- Control Tasks for the Section ``Dynamics'' -- References -- 4 Theory of Impact -- 4.1 Impact Phenomenon and Its Main Characteristics -- 4.2 Basic Theorems of the Theory of Impact -- 4.3 Impact of a Point on a Stationary Surface -- 4.4 Experimental Determination of the Recovery Factor -- 4.5 Impact of Two Bodies -- 4.6 Carnot's Theorem -- 4.7 Rotating Body Blow -- Self-Test Questions -- Self-Test Questions -- Control Tasks for the Section ``Theory of Impact'' -- Variant 1 -- Variant 2 -- Variant 3 -- Variant 4 -- Variant 5 -- Variant 6 -- Variant 7 -- Variant 8 -- Variant 9 -- Variant 10 -- Example of Completing a Task -- References. ; 5 Elements of Analytic Mechanics -- 5.1 The Principle of Possible Movements -- 5.2 Generalized Coordinates: Generalized Forces -- 5.3 The Case of Conservative Forces -- 5.4 Equilibrium Conditions of the System in Generalized Coordinates -- 5.5 General Equation of System Dynamics -- 5.6 Equations in generalized coordinates -- 5.6.1 The Case of Conservative Forces -- Self-Test Questions -- Self-Test Questions -- Control Tasks for the Section ``Analytical Mechanics'' -- Task -- Investigation of the Equations of Motion of a System with Two Degrees of Freedom by the Method of Lagrange Equations of the Second Kind (Example) -- References -- 6 Dynamics of Controlled Systems -- 6.1 Mathematical Model of the Controlled System -- 6.2 Basic Information About Functionals and Function Spaces -- 6.3 Variations of Comparison Curves and Functionals -- 6.4 Statement of the Mayer Variational Problem -- 6.5 The Maximum Principle -- 6.6 Erdmann-Weierstrass Conditions: First Integral -- 6.7 The Simplest Problem of Optimal Performance -- 6.7.1 Building a Mathematical Model -- 6.7.2 Border Conditions -- 6.7.3 Functional -- 6.7.4 Getting Additional Ratios -- 6.7.5 Traction Control Program -- 6.7.6 Integration of Differential Equations of the Problem -- 6.7.7 Completion of the Integration of Problem Equations -- 6.8 Flying the Drone to the Maximum Range -- 6.8.1 Building a Mathematical Model -- 6.8.2 Border Conditions -- 6.8.3 Minimizing Functional -- 6.8.4 Additional Ratios -- 6.8.5 Necessary Conditions for a Strong andWeak Minimum -- 6.8.6 Preparing to Integrate the Aggregate Equations of the Problem -- 6.8.7 Traction Control Program -- 6.8.8 Completion of the Integration of the Differential Equations of the Problem -- Self-Test Questions -- Self-Test Questions -- References -- 7 Stability of Mechanical Systems -- 7.1 Stability and Instability. ; 7.2 Work and Classification of Forces -- 7.3 Stability with Conservative and Dissipative Forces -- 7.4 Lyapunov-Chetaev Theorem -- 7.5 Instability in the First Approximation -- 7.6 Critical Load -- 7.7 The Theorem on Stability by the First Approximation -- 7.8 The Raus-Hurwitz Criterion -- 7.9 Main Types of Stability Loss -- 7.10 Methods for Determining Critical Load -- 7.11 The Perturbed Motion of the Compressed Rod -- 7.12 Stability Under Non-conservative Load (Example) -- 7.12.1 Equations of Perturbed Motion -- 7.12.2 Area of Valid Stability -- 7.12.3 Investigation of the Value μ, (Formula (7.31)) -- 7.12.4 Investigation of the Effect of Friction -- 7.12.5 The Influence of the Spacing of the End Masses -- Self-Test Questions -- Self-Test Questions -- Stability of the Equilibrium State of a Conservative Mechanical System -- References -- Part II Elements of the Theory of Mechanisms and Machines -- 8 Basic Concepts -- 8.1 Conditional Classification of Machines -- 8.2 Components of the Mechanism -- 8.3 Kinematic Pairs and Chains -- Self-Test Questions -- Self-Test Questions -- References -- 9 Structural Analysis of Mechanisms -- 9.1 The Degree of Mobility of the Kinematic Chain -- 9.2 Structural Classification of Mechanisms -- 9.2.1 Example of a Structural Analysis of a Mechanism -- Self-Test Questions -- Self-Test Questions -- References -- 10 Kinematic Analysis of Mechanisms -- 10.1 Objectives and Methods of Kinematic Analysis -- 10.2 Building Plans for the Provisions of the Mechanism -- 10.3 Kinematic Diagrams -- 10.3.1 Displacement Diagrams -- 10.3.2 Plotting Velocity and Acceleration Diagrams -- 10.4 Speed and Acceleration Plans -- 10.4.1 Building a Speed Plan -- 10.4.2 Building an Acceleration Plan -- 10.5 Analytical Study of the Kinematics of Mechanisms -- Questions for Self-Test -- References -- 11 Dynamic Analysis of Mechanisms. ; 11.1 Classification of Forces -- 11.2 Kinetostatics Problems -- 11.3 Methods of Force Calculation of Mechanisms -- 11.3.1 Force Plans Method -- 11.3.2 Decomposition of Forces -- 11.3.3 Analytical Method -- 11.3.4 Determination of Balancing Force -- Self-Test Questions -- Self-Test Questions -- References -- Part III Strength of Materials -- 12 Initial Concepts and Definitions -- 12.1 Objectives of the Course on Strength of Materials -- 12.2 External Forces: The Saint-Venant Principle -- 12.3 The Simplest Stress States -- 12.4 Deformations and Displacements -- 12.5 Material Testing: Hooke's Law -- Self-Test Questions -- Self-Test Questions -- References -- 13 Calculation of Parts in Tension-Compression -- 13.1 Internal Tensile-Compressive Forces -- 13.2 Stresses -- 13.3 Determination of Deformations and Displacements -- 13.4 Potential Deformation Energy of the Body -- 13.5 Strength Calculations -- 13.6 Statically Indeterminate Tasks -- 13.7 Calculation by permissible loads -- Self-Test Questions -- Self-Test Questions -- References -- 14 Tense State: Strength Theories -- 14.1 Material Strength Hypotheses -- 14.2 Types of Stress -- 14.3 Generalized Hooke's Law -- 14.4 Plane State -- 14.4.1 General Provisions -- 14.4.2 Analysis of the Plane Stress State -- 14.5 Strength Theories -- 14.5.1 Question Statement -- 14.5.2 Working Strength Theories -- Self-Test Questions -- Self-Test Questions -- References -- 15 Shear and Torsion -- 15.1 Shear -- 15.2 Torsion of the Circular Shaft -- 15.3 Calculation of Shafts for Strength and Rigidity -- Self-Test Questions -- Self-Test Questions -- References -- 16 Bending -- 16.1 The Concept of Bending Deformation -- 16.2 Internal Bending Forces -- 16.2.1 Example of Defining Internal Effort -- 16.3 Differential Bending Dependencies -- 16.4 Normal Bending Stresses -- 16.5 Tangential Bending Stresses. ; 16.6 Strength Calculation Based on Permissible Stresses.
• Titolo autorizzato: Theoretical and applied mechanics
• ISBN: 3-031-09312-7
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910624305903321
• Lo trovi qui: Univ. Federico II