1Introduction to MATLAB
1014.3 Kinematics of Rigid Bodies in Two Dimensions
21.1 Getting Started with MATLAB
1024.3.1 Position Analysis
31.1.1 Introduction to MATLAB
1034.3.2 Velocity Analysis
41.1.2 Installation and Setup
1044.3.3 Acceleration Analysis
51.1.3 MATLAB Basics
1054.3.4 MATLAB Implementation
61.1.4 MATLAB Documentation and Help Resources
1064.4 Kinematics of Rigid Bodies in Three Dimensions
71.1.5 Interactive MATLAB Exercises
1074.4.1 Position of a Rigid Body in Three Dimensions: Understanding Spatial Localization
81.1.6 MATLAB for Mechanics Applications
1084.4.2 Orientation of a Rigid Body in Three Dimensions: Describing Spatial Configuration
91.2 MATLAB Fundamentals
1094.4.3 Velocity of a Rigid Body in Three Dimensions: Analyzing Spatial Motion
101.2.1 Introduction to MATLAB Interface
1104.4.4 Acceleration of a Rigid Body in Three Dimensions: Exploring Dynamic Changes
111.2.2 MATLAB Syntax and Commands
1114.4.5 Application of Velocity and Acceleration in MATLAB: Analyzing Spatial Motion Dynamics
121.2.3 Data Types and Operations
112Conclusion
131.2.4 Control Flow Structures
113Rigid Body Dynamics
141.2.5 MATLAB Plotting and Visualization
1145.1 Torque and Angular Momentum
151.3 Basic Operations and Functions
1155.1.1 Definition of Torque
161.3.1 Introduction to Basic Operations
1165.1.2 Mathematical Representation of Torque
171.3.2 Arithmetic Operations
1175.1.3 Significance of Torque
181.3.3 Relational and Logical Operations
1185.1.4 Definition of Angular Momentum
191.3.4 Element-wise Operations
1195.1.5 Mathematical Representation of Angular Momentum
201.3.5 Built-in Functions
1205.1.6 Significance of Angular Momentum
211.3.6 Custom Functions
1215.2 Moment of Inertia: Understanding Rotational Mass Distribution
221.3.7 Function Handles and Anonymous Functions
1225.2.1 Definition and Concept of Moment of Inertia: Quantifying Rotational Mass Distribution
231.3.8 Vectorization and Efficiency
1235.2.2 Calculation Methods for Moment of Inertia: Analyzing Mass Distribution in Rotating Bodies
241.4 Plotting and Visualization in MATLAB
1245.2.3 Physical Significance of Moment of Inertia: Understanding Rotational Motion Behavior
251.4.1 Basic Plotting Functions
1255.2.4 Parallel and Perpendicular Axis Theorems: Simplifying Moment of Inertia Calculations
261.4.2 Customization Options
1265.2.5 Applications of Moment of Inertia: Engineering Insights and Design Considerations
271.4.3 Multiple Axes and Subplots
1275.3 Equations of Motion for Rotating Bodies
281.4.4 Annotation and Labeling
1285.3.1 Angular Momentum and Torque
291.4.5 Exporting and Saving Plots
1295.3.2 Euler’s Equations of Motion
301.4.6 Advanced Plotting Techniques
1305.3.3 Implementations Using MATLAB
311.4.7 Interactive Plotting and GUIs
1315.4 Conservation of Angular Momentum: Understanding Rotational Motion Principles
32Particle Kinematics
1325.4.1 Definition and Concept of Angular Momentum: Exploring Rotational Motion Quantities
332.1 Position, Displacement, and Distance
1335.4.2 Conservation Principle of Angular Momentum: Maintaining Rotational Equilibrium
342.1.1 Position
1345.4.3 Applications of Angular Momentum Conservation: Engineering and Scientific Insights
352.1.2 Displacement
1355.4.4 Practical Considerations in Angular Momentum Conservation: Engineering Insights
362.1.3 Distance
1365.4.5 Computational Analysis of Angular Momentum Conservation: Tools and Techniques
372.1.4 MATLAB Implementation
137Conclusion
382.1.5 Visualization
138Oscillatory Motion
392.2 Velocity and Speed
1396.1 Simple Harmonic Motion: Understanding Oscillatory Dynamics
402.2.1 Definition of Velocity and Speed
1406.1.1 Definition and Characteristics of Simple Harmonic Motion (SHM)
412.2.2 Instantaneous and Average Velocity
1416.1.2 Equation of Motion for Simple Harmonic Motion
422.2.3 Units and Dimensional Analysis
1426.1.3 Energy Considerations in Simple Harmonic Motion
432.2.4 Graphical Representation
1436.1.4 Period and Frequency of Simple Harmonic Motion
442.2.5 Application of Velocity and Speed in MATLAB
1446.1.5 Phase and Amplitude in Simple Harmonic Motion
452.3 Acceleration
1456.1.6 Practical Applications of Simple Harmonic Motion
462.3.1 Definition of Acceleration
1466.2 Damped and Forced Oscillations
472.3.2 Types of Acceleration
1476.2.1 Damped Oscillations: 6.2.2 Forced Oscillations
482.3.3 Calculation of Acceleration
1486.3 Energy in Oscillatory Systems: Understanding the Dynamics of Energy Exchange
492.3.4 Visualization of Acceleration
1496.3.1 Conservation of Mechanical Energy in Oscillatory Systems
502.3.5 Applications of Acceleration
1506.3.2 Kinetic Energy in Oscillatory Systems: Understanding Motion Dynamics
512.3.6 MATLAB Implementation
1516.3.3 Potential Energy in Oscillatory Systems: Exploring Energy Storage Mechanisms
522.4 Motion in One Dimension
1526.3.4 Energy Exchange during Oscillation: Understanding the Interplay of Kinetic and Potential Energies
532.4.1 Displacement and Distance
1536.3.5 Practical Implications of Energy Exchange in Oscillatory Systems
542.4.2 Velocity
1541. Enhanced System Design:
552.4.3 Acceleration
1552. Resonance Mitigation and Control:
562.4.4 Kinematic Equations
1563. Energy-Efficient Technologies:
572.4.5 MATLAB Implementation
1574. Control and Stability:
58Particle Dynamics
1585. Predictive Maintenance and Health Monitoring:
593.1 Newton’s Laws of Motion
1596. Innovation and Advancement:
603.1.1 Newton’s First Law: Law of Inertia
1606.4 MATLAB Simulations of Oscillatory Motion
613.1.2 Newton’s Second Law: Law of Acceleration
1616.4.1 Introduction to MATLAB Simulations
623.1.3 Newton’s Third Law: Law of Action and Reaction
1626.4.2 Solving Differential Equations
633.2 Force and Inertia
1636.4.3 Visualization of Oscillatory Motion
643.2.1 Force
1646.4.4 Analysis of Oscillatory Systems
653.2.2 Inertia
1656.4.5 Case Studies and Examples
663.2.3 Newton’s Laws of Motion
1666.4.6 Optimization and Control
671. Newton’s First Law of Motion (Law of Inertia):: 2. Newton’s Second Law of Motion (Law of Acceleration):
167Conclusion
683.3 Momentum and Impulse
168Fluid Mechanics Basics
693.3.1 Momentum
1697.1 Properties of Fluids: Understanding the Characteristics of Fluids
703.3.2 Impulse
1707.1.1 Density: Understanding the Fundamental Property of Fluids
713.3.3 Conservation of Momentum
1717.1.2 Viscosity: Exploring the Internal Resistance of Fluids
723.3.4 Practical Applications of Momentum and Impulse
1727.1.3 Pressure: Unveiling the Force Exerted by Fluids
731. Automotive Engineering:
1737.1.4 Buoyancy: Exploring the Upward Force in Fluids
742. Sports Biomechanics:
1747.1.5 Surface Tension: Unraveling the Cohesive Force at Fluid Interfaces
753. Aerospace Engineering:: 4. Biomedical Engineering:
1757.2 Fluid Statics: Pressure and Buoyancy
763.3.5 MATLAB Implementation of Momentum and Impulse Analysis
1767.2.1 Pressure in Fluids
771. Numerical Integration:
1777.2.2 Buoyancy Force
782. Simulation of Dynamic Systems:
1787.2.3 Applications of Buoyancy Force
793. Visualization of Motion Dynamics:
1797.3 Fluid Flow: Continuity Equation and Bernoulli’s Principle
804. Optimization and Design:
1807.3.1 Continuity Equation: Ensuring Conservation of Mass
815. Educational Tools:
1817.3.2 Bernoulli’s Principle: Unveiling the Conservation of Energy in Fluid Flow
826. Research and Development:
1827.3.3 Applications and Engineering Implications of Bernoulli’s Principle and the Continuity Equation
833.4 Work and Energy
1831. Hydraulic Engineering:
843.4.1 Work
1842. Aerospace Engineering:
853.4.2 Kinetic Energy
1853. HVAC Systems:
863.4.3 Potential Energy
1864. Environmental Engineering:
87Conclusion
1875. Medical Devices:
88Rigid Body Kinematics
1886. Transportation:
894.1 Rotation and Translation
1897.4 Viscosity and Reynolds Number
904.1.1 Definition of Rotation
1907.4.1 Viscosity: 7.4.2 Reynolds Number
914.1.2 Representation of Rotations
1917.5 MATLAB Applications in Fluid Mechanics
924.1.3 Properties of Rotations
1927.5.1 Solving Fluid Flow Equations Using MATLAB
934.1.4 Definition of Translation
1937.5.2 Computational Fluid Dynamics (CFD) Simulations Using MATLAB
944.1.5 Representation of Translations
1947.5.3 Fluid Flow Visualization Using MATLAB
954.1.6 Properties of Translations
1957.5.4 Design Optimization Using MATLAB in Fluid Mechanics
964.2 Angular Velocity and Angular Acceleration
1967.5.5 Educational Tools and Tutorials in Fluid Mechanics Using MATLAB
974.2.1 Angular Velocity: Understanding Rotational Speed and Direction
1977.5.6 Research and Development Applications of MATLAB in Fluid Mechanics
984.2.2 Angular Acceleration: Exploring Changes in Rotational Motion
198Conclusion
994.2.3 Relationship between Angular Velocity and Angular Acceleration: Understanding Rotational Dynamics
199Glossary
1004.2.4 Application of Angular Velocity and Angular Acceleration in MATLAB: Analyzing Rotational Motion
200Index
