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Advanced Dynamics Rigid Body, Multibody, and Aerospace Applications

• Part I Fundamentals
• Fundamentals of Kinematics
• Coordinate Frame and Position Vector
• Coordinate Frame and Position Vector
• Vector Definition
• Vector Algebra
• Vector Multiplication
• Index Notation
• Orthogonal Coordinate Frames
• Orthogonality Condition
• Unit Vector
• Direction of Unit Vectors
• Differential Geometry
• Space Curve
• Surface and Plane
• Motion Path Kinematics
• Vector Function and Derivative
• Velocity and Acceleration
• Natural Coordinate Frame
• Fields
• Surface and Orthogonal Mesh
• Scalar Field and Derivative
• Vector Field and Derivative
• Key Symbols
• Exercises
• Fundamentals of Dynamics
• Laws of Motion
• Equation of Motion
• Force and Moment
• Motion Equation
• Special Solutions
• Force Is a Function of Time, F = F (t)
• Force Is a Function of Position, F = F (x)
•  Elliptic Functions
• Force Is a Function of Velocity, F = F (v)
• Spatial and Temporal Integrals
• Spatial Integral: Work and Energy
• Temporal Integral: Impulse and Momentum
• Application of Dynamics
• Modeling
• Equations of Motion
• Dynamic Behavior and Methods of Solution
• Key Symbols
• Exercises
• Part II Geometric Kinematics
• Coordinate Systems
• Cartesian Coordinate System
• Cylindrical Coordinate System
• Spherical Coordinate System
• Nonorthogonal Coordinate Frames
• Reciprocal Base Vectors
• Reciprocal Coordinate Frame
• Inner and Outer Vector Product
• Kinematics in Oblique Coordinate Frames
• Curvilinear Coordinate System
• Principal and Reciprocal Base Vectors
• Principal–Reciprocal Transformation
• Curvilinear Geometry
• Curvilinear Kinematics
• Kinematics in Curvilinear Coordinates
• Key Symbols
• Exercises
• Rotation Kinematics
• Rotation About Global Cartesian Axes
• Successive Rotations About Global Axes
• Global Roll–Pitch–Yaw Angles
• Rotation About Local Cartesian Axes
• Successive Rotations About Local Axes
• Euler Angles
• Local Roll–Pitch–Yaw Angles
• Local versus Global Rotation
• General Rotation
• Active and Passive Rotations
• Rotation of Rotated Body
• Key Symbols
• Exercises
• Orientation Kinematics
• Axis–Angle Rotation
• Euler Parameters
• Quaternion
• Spinors and Rotators
• Problems in Representing Rotations
• Rotation Matrix
• Axis–Angle
• Euler Angles
• Quaternion and Euler Parameters
• Composition and Decomposition of Rotations
• Composition of Rotations
• Decomposition of Rotations
• Key Symbols
• Exercises
• Motion Kinematics
• Rigid-Body Motion
• Homogeneous Transformation
• Inverse and Reverse Homogeneous Transformation
• Compound Homogeneous Transformation
• Screw Motion
• Inverse Screw
• Compound Screw Transformation
• Plucker Line Coordinate ¨
• Geometry of Plane and Line
• Moment
• Angle and Distance
• Plane and Line
• Screw and Plucker Coordinate
• Key Symbols
• Exercises
• Multibody Kinematics
• Multibody Connection
• Denavit–Hartenberg Rule
• Forward Kinematics
• Assembling Kinematics
• Order-Free Rotation
• Order-Free Transformation
• Forward Kinematics by Screw
• Caster Theory in Vehicles
• Inverse Kinematics
• Key Symbols
• Exercises
• Part III Derivative Kinematics
• Velocity Kinematics
• Angular Velocity
• Time Derivative and Coordinate Frames
• Multibody Velocity
• Velocity Transformation Matrix
• Derivative of a Homogeneous Transformation Matrix
• Multibody Velocity
• Forward-Velocity Kinematics
• Jacobian-Generating Vector
• Inverse-Velocity Kinematics
• Key Symbols
• Exercises
• Acceleration Kinematics
• Angular Acceleration
• Second Derivative and Coordinate Frames
• Multibody Acceleration
• Particle Acceleration
• Mixed Double Derivative
• Acceleration Transformation Matrix
• Forward-Acceleration Kinematics
• Inverse-Acceleration Kinematics
• Key Symbols
• Exercises
• Constraints
• Homogeneity and Isotropy
• Describing Space
• Configuration Space
• Event Space
• State Space
• State–Time Space
• Kinematic Spaces
• Holonomic Constraint
• Generalized Coordinate
• Constraint Force
• Virtual and Actual Works
• Nonholonomic Constraint
• Nonintegrable Constraint
• Inequality Constraint
• Differential Constraint
• Generalized Mechanics
• Integral of Motion
• Methods of Dynamics
• Lagrange Method
• Gauss Method
• Hamilton Method
• Gibbs–Appell Method
• Kane Method
• Nielsen Method
• Key Symbols
• Exercises
• Part IV Dynamics
• Rigid Body and Mass Moment
• Rigid Body
• Elements of the Mass Moment Matrix
• Transformation of Mass Moment Matrix
• Principal Mass Moments
• Key Symbols
• Exercises
• Rigid-Body Dynamics
• Rigid-Body Rotational Cartesian Dynamics
•  Rigid-Body Rotational Eulerian Dynamics
• Rigid-Body Translational Dynamics
• Classical Problems of Rigid Bodies
• Torque-Free Motion
• Spherical Torque-Free Rigid Body
• Axisymmetric Torque-Free Rigid Body
• Asymmetric Torque-Free Rigid Body
• General Motion
• Multibody Dynamics
• Recursive Multibody Dynamics
• Key Symbols
• Exercises
• Lagrange Dynamics
• Lagrange Form of Newton Equations
• Lagrange Equation and Potential Force
• Variational Dynamics
• Hamilton Principle
• Lagrange Equation and Constraints
• Conservation Laws
• Conservation of Energy
• Conservation of Momentum
• Generalized Coordinate System
• Multibody Lagrangian Dynamics
• Key Symbols
• Exercises

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