The Resource Intermediate dynamics : a linear algebraic approach, R.A. Howland, (electronic resource)

Intermediate dynamics : a linear algebraic approach, R.A. Howland, (electronic resource)

Label
Intermediate dynamics : a linear algebraic approach
Title
Intermediate dynamics
Title remainder
a linear algebraic approach
Statement of responsibility
R.A. Howland
Creator
Contributor
Subject
Genre
Language
eng
Member of
Cataloging source
GW5XE
http://library.link/vocab/creatorDate
1943-
http://library.link/vocab/creatorName
Howland, R. A.
Dewey number
531/.11
Illustrations
illustrations
Index
index present
LC call number
QA846
LC item number
.H69 2006eb
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
SpringerLink (Online service)
Series statement
Mechanical engineering series
http://library.link/vocab/subjectName
  • Dynamics
  • Algebras, Linear
Label
Intermediate dynamics : a linear algebraic approach, R.A. Howland, (electronic resource)
Link
Instantiates
Publication
Bibliography note
Includes bibliographical references and index
Color
multicolored
Contents
  • 1.1.1. The
  • "algebra" of vector spaces
  • 1.2. The
  • basis of a vector space
  • 1.2.1.
  • Spanning sets
  • 1.2.2.
  • Linear independence
  • A
  • test for linear independence of n-tuples : reduction to Echelon form
  • Preface
  • 1.2.3.
  • Bases and the dimension of a vector space
  • Theorems on dimension
  • 1.3. The
  • representation of vectors
  • 1.3.1.
  • N-tupe representations of vectors
  • 1.3.2.
  • Representations and units
  • 1.3.3.
  • [pt]. 1.
  • isomorphisms among vector spaces of the same dimension
  • 2.
  • Linear transformations on vector spaces
  • 2.1.
  • Matrices
  • 2.1.1. The
  • "partitioning" and rank of matrices
  • The
  • rank of a matrix
  • 2.1.2.
  • Linear algebra
  • Operations on matrices
  • Inner product
  • Transpose of a matrix product
  • Block multiplication of partitioned matrices
  • Elementary operations through matrix products
  • 2.2.
  • Linear transformations
  • Domain and range of [linear] transformation and their dimension
  • 2.2.1.
  • Linear transformations : basis and representation
  • Prologue
  • Dyadics
  • 2.2.2.
  • Null space of a linear transformation
  • Dimension of the null space
  • Relation between dimensions of domain, range, and null space
  • 2.3.
  • Solution of linear systems
  • "Skips" and the null space
  • 2.3.1.
  • Theory of linear equations
  • 1.
  • Homogeneous linear equations
  • Non-homogeneous linear equations
  • 2.4.
  • Linear operators - differential equations --
  • Vector spaces
  • 1.1.
  • Vectors
  • determinant of a square matrix
  • Properties of the determinant
  • 3.3.
  • Classification of square matrices
  • 3.3.1.
  • Orthogonal matrices - rotations
  • 3.3.2. The
  • orientation of non-orthonormal bases
  • 3.4.
  • Linear systems : n equations in n unknowns
  • 3.
  • 3.5.
  • Eigenvalues and eigenvectors of a square matrix
  • 3.5.1.
  • Linear independence of eigenvectors
  • 3.5.2. The
  • Cayley-Hamilton theorem
  • 3.5.3.
  • Generalized eigenvectors
  • 3.5.4.
  • Application of eigenvalues/eigenvectors
  • Special case - square matrices
  • 3.6.
  • Application - basis transformations
  • 3.6.1.
  • General basis transformations--
  • Successive basis transformations
  • 3.6.2.
  • Basis rotations
  • 3.7.
  • Normal forms of square matrices
  • 3.7.1.
  • The
  • Linearly independent eigenvectors - diagonalization
  • Diagonalization of real symmetric matrices
  • 3.7.2.
  • Linearly dependent eigenvectors - Jordan normal form --
  • "algebra" of square matrices
  • 3.1. The
  • inverse of a square matrix
  • Properties of the inverse
  • 3.2. The
  • General motion of a rigid body
  • Differentials
  • 4.1.2.
  • Rotation of a rigid body
  • Differential rigid body rotation
  • Angular velocity and acceleration
  • Time derivative of a unit vector with respect to rotation
  • 4.2.
  • Euler angles
  • 4.2.1.
  • [pt]. 2.
  • Direction angles and cosines
  • Vector description
  • Coordinate system description
  • 4.2.2.
  • Euler angles
  • Vector description
  • Coordinate system description
  • 4.3.
  • Moving coordinate systems -
  • 4.3.1.
  • 3-D rigid body dynamics
  • Relative motion : points
  • 4.3.2.
  • Relative motion : coordinate systems
  • Time derivatives in rotating coordinate systems
  • Applications of theorem 4.3.1
  • Rotating coordinate system equations
  • Distinction between the "A/B" and "rel" quantities
  • The
  • need for rotating coordinate systems
  • 4.4.
  • Prologue
  • Machine kinematics
  • 4.4.1.
  • Motion of a single body
  • A
  • useful trick
  • The
  • non-slip condition
  • The
  • instantaneous center of zero velocity--
  • 4.5.2.
  • 4.
  • Kinematic constraints imposed by linkages
  • Clevis connections
  • Ball-and-socket connections
  • 4.4.3.
  • Motion of multiple rigid bodies ("machines")
  • Curved interconnections
  • General analysis of universal joints --
  • Kinematics
  • 4.1.
  • Motion of a rigid body
  • 4.1.1.
  • Energy
  • A
  • caveat regarding conservation
  • 5.1.2
  • Particle system kinetics
  • Kinetics relative to a fixed system
  • Kinetics relative to the center of mass
  • 5.2.
  • Equations of motion for rigid bodies
  • 5.2.1.
  • 5.
  • angular momentum of a rigid body - the inertia tensor
  • Properties of the inertia tensor
  • Principal axes
  • 5.2.2.
  • Equations of motion
  • Forces/moments at interconnections
  • Determination of the motion of a system
  • 5.2.3. A
  • special case - the gyroscope
  • Gyroscope coordinate axes and angular velocities
  • Kinetics
  • Equations of motion
  • Special case - moment-free gyroscopic motion
  • General case - gyroscope with moment
  • 5.3.
  • Dynamic stability
  • 5.4.
  • Alternatives to direct integration
  • 5.4.1.
  • Energy
  • Kinetic energy
  • 5.1.
  • Work
  • Energy principles
  • 5.4.2.
  • Momentum - -
  • 5.4.3
  • Conservation application in general
  • Epilogue --
  • Particles and systems of particles
  • 5.1.1.
  • Particle kinetics
  • Linear momentum and its equation of motion
  • Angular momentum and its equation of motion
  • Scalar formulations and constraints
  • 6.3.
  • Concepts from virtual work in statics
  • 7.
  • Lagrangian dynamics : kinematics
  • 7.1.
  • Background : position and constraints
  • Categorization of differential constraints
  • Constraints and linear independence
  • 7.2.
  • [pt]. 3.
  • Virtual displacements
  • 7.3.
  • Kinematic vs. kinetic constraints
  • 7.4.
  • Generalized coordinates
  • Derivatives a r and v with respect to generalized coordinates and velocities
  • 8.
  • Lagrangian dynamics : kinetics
  • 8.1.
  • Arbitrary forces : Euler-Lagrange equations
  • Analytical dynamics
  • Notes on the Euler-Lagrange equations--
  • 8.2.
  • conservative forces : Lagrange equations
  • Properties of the Lagrangian
  • 8.3.
  • Differential constraints
  • 8.3.1.
  • algebraic approach to differential constraints
  • 8.3.2.
  • Lagrange multipliers
  • Prologue
  • Interpretation of the Lagrange multipliers
  • 8.4.
  • Time as a coordinate --
  • 6.
  • Analytical dynamics : perspective
  • 6.1.
  • Vector formulations and constraints
  • 6.2.
  • 10.
  • Hamiltonian dynamics
  • 10.1. The
  • variables
  • Solution for q̇ (q, p; t)
  • 10.2. The
  • equations of motion
  • 10.2.1.
  • Legendre transformations
  • 10.2.2.
  • 9.
  • Q and p as Lagrangian variables
  • 10.2.3. An
  • important property of the Hamiltonian
  • 10.3.
  • Integrals of the motion
  • 10.4.
  • Canonical transformations
  • 10.5.
  • Generating functions
  • 10.6.
  • Integrals of motion
  • Transformation solution of Hamiltonians
  • 10.7.
  • Separability
  • 10.7.1. The
  • Hamilton-Jacobi equation
  • 10.7.2.
  • Separable variables
  • Special case - ignorable coordinates
  • 10.8.
  • Constraints in Hamiltonian systems
  • 9.1.
  • 10.9.
  • Time as a coordinate in Hamiltonians
  • Epilogue
  • Index
  • Integrals of the motion
  • 9.2.
  • Jacobi's integral - an energy-like integral
  • 9.3.
  • "Ignorable coordinates" and integrals
Dimensions
24 cm.
Dimensions
unknown
Extent
xix, 540 p.
Form of item
electronic
Isbn
9780387283166
Other physical details
ill.
Reproduction note
Electronic reproduction.
Specific material designation
remote
Stock number
978-0-387-28059-2
System control number
  • 3172498-01okla_normanlaw
  • (SIRSI)3172498
  • (Sirsi) o262691121
  • (OCoLC)262691121
Label
Intermediate dynamics : a linear algebraic approach, R.A. Howland, (electronic resource)
Link
Publication
Bibliography note
Includes bibliographical references and index
Color
multicolored
Contents
  • 1.1.1. The
  • "algebra" of vector spaces
  • 1.2. The
  • basis of a vector space
  • 1.2.1.
  • Spanning sets
  • 1.2.2.
  • Linear independence
  • A
  • test for linear independence of n-tuples : reduction to Echelon form
  • Preface
  • 1.2.3.
  • Bases and the dimension of a vector space
  • Theorems on dimension
  • 1.3. The
  • representation of vectors
  • 1.3.1.
  • N-tupe representations of vectors
  • 1.3.2.
  • Representations and units
  • 1.3.3.
  • [pt]. 1.
  • isomorphisms among vector spaces of the same dimension
  • 2.
  • Linear transformations on vector spaces
  • 2.1.
  • Matrices
  • 2.1.1. The
  • "partitioning" and rank of matrices
  • The
  • rank of a matrix
  • 2.1.2.
  • Linear algebra
  • Operations on matrices
  • Inner product
  • Transpose of a matrix product
  • Block multiplication of partitioned matrices
  • Elementary operations through matrix products
  • 2.2.
  • Linear transformations
  • Domain and range of [linear] transformation and their dimension
  • 2.2.1.
  • Linear transformations : basis and representation
  • Prologue
  • Dyadics
  • 2.2.2.
  • Null space of a linear transformation
  • Dimension of the null space
  • Relation between dimensions of domain, range, and null space
  • 2.3.
  • Solution of linear systems
  • "Skips" and the null space
  • 2.3.1.
  • Theory of linear equations
  • 1.
  • Homogeneous linear equations
  • Non-homogeneous linear equations
  • 2.4.
  • Linear operators - differential equations --
  • Vector spaces
  • 1.1.
  • Vectors
  • determinant of a square matrix
  • Properties of the determinant
  • 3.3.
  • Classification of square matrices
  • 3.3.1.
  • Orthogonal matrices - rotations
  • 3.3.2. The
  • orientation of non-orthonormal bases
  • 3.4.
  • Linear systems : n equations in n unknowns
  • 3.
  • 3.5.
  • Eigenvalues and eigenvectors of a square matrix
  • 3.5.1.
  • Linear independence of eigenvectors
  • 3.5.2. The
  • Cayley-Hamilton theorem
  • 3.5.3.
  • Generalized eigenvectors
  • 3.5.4.
  • Application of eigenvalues/eigenvectors
  • Special case - square matrices
  • 3.6.
  • Application - basis transformations
  • 3.6.1.
  • General basis transformations--
  • Successive basis transformations
  • 3.6.2.
  • Basis rotations
  • 3.7.
  • Normal forms of square matrices
  • 3.7.1.
  • The
  • Linearly independent eigenvectors - diagonalization
  • Diagonalization of real symmetric matrices
  • 3.7.2.
  • Linearly dependent eigenvectors - Jordan normal form --
  • "algebra" of square matrices
  • 3.1. The
  • inverse of a square matrix
  • Properties of the inverse
  • 3.2. The
  • General motion of a rigid body
  • Differentials
  • 4.1.2.
  • Rotation of a rigid body
  • Differential rigid body rotation
  • Angular velocity and acceleration
  • Time derivative of a unit vector with respect to rotation
  • 4.2.
  • Euler angles
  • 4.2.1.
  • [pt]. 2.
  • Direction angles and cosines
  • Vector description
  • Coordinate system description
  • 4.2.2.
  • Euler angles
  • Vector description
  • Coordinate system description
  • 4.3.
  • Moving coordinate systems -
  • 4.3.1.
  • 3-D rigid body dynamics
  • Relative motion : points
  • 4.3.2.
  • Relative motion : coordinate systems
  • Time derivatives in rotating coordinate systems
  • Applications of theorem 4.3.1
  • Rotating coordinate system equations
  • Distinction between the "A/B" and "rel" quantities
  • The
  • need for rotating coordinate systems
  • 4.4.
  • Prologue
  • Machine kinematics
  • 4.4.1.
  • Motion of a single body
  • A
  • useful trick
  • The
  • non-slip condition
  • The
  • instantaneous center of zero velocity--
  • 4.5.2.
  • 4.
  • Kinematic constraints imposed by linkages
  • Clevis connections
  • Ball-and-socket connections
  • 4.4.3.
  • Motion of multiple rigid bodies ("machines")
  • Curved interconnections
  • General analysis of universal joints --
  • Kinematics
  • 4.1.
  • Motion of a rigid body
  • 4.1.1.
  • Energy
  • A
  • caveat regarding conservation
  • 5.1.2
  • Particle system kinetics
  • Kinetics relative to a fixed system
  • Kinetics relative to the center of mass
  • 5.2.
  • Equations of motion for rigid bodies
  • 5.2.1.
  • 5.
  • angular momentum of a rigid body - the inertia tensor
  • Properties of the inertia tensor
  • Principal axes
  • 5.2.2.
  • Equations of motion
  • Forces/moments at interconnections
  • Determination of the motion of a system
  • 5.2.3. A
  • special case - the gyroscope
  • Gyroscope coordinate axes and angular velocities
  • Kinetics
  • Equations of motion
  • Special case - moment-free gyroscopic motion
  • General case - gyroscope with moment
  • 5.3.
  • Dynamic stability
  • 5.4.
  • Alternatives to direct integration
  • 5.4.1.
  • Energy
  • Kinetic energy
  • 5.1.
  • Work
  • Energy principles
  • 5.4.2.
  • Momentum - -
  • 5.4.3
  • Conservation application in general
  • Epilogue --
  • Particles and systems of particles
  • 5.1.1.
  • Particle kinetics
  • Linear momentum and its equation of motion
  • Angular momentum and its equation of motion
  • Scalar formulations and constraints
  • 6.3.
  • Concepts from virtual work in statics
  • 7.
  • Lagrangian dynamics : kinematics
  • 7.1.
  • Background : position and constraints
  • Categorization of differential constraints
  • Constraints and linear independence
  • 7.2.
  • [pt]. 3.
  • Virtual displacements
  • 7.3.
  • Kinematic vs. kinetic constraints
  • 7.4.
  • Generalized coordinates
  • Derivatives a r and v with respect to generalized coordinates and velocities
  • 8.
  • Lagrangian dynamics : kinetics
  • 8.1.
  • Arbitrary forces : Euler-Lagrange equations
  • Analytical dynamics
  • Notes on the Euler-Lagrange equations--
  • 8.2.
  • conservative forces : Lagrange equations
  • Properties of the Lagrangian
  • 8.3.
  • Differential constraints
  • 8.3.1.
  • algebraic approach to differential constraints
  • 8.3.2.
  • Lagrange multipliers
  • Prologue
  • Interpretation of the Lagrange multipliers
  • 8.4.
  • Time as a coordinate --
  • 6.
  • Analytical dynamics : perspective
  • 6.1.
  • Vector formulations and constraints
  • 6.2.
  • 10.
  • Hamiltonian dynamics
  • 10.1. The
  • variables
  • Solution for q̇ (q, p; t)
  • 10.2. The
  • equations of motion
  • 10.2.1.
  • Legendre transformations
  • 10.2.2.
  • 9.
  • Q and p as Lagrangian variables
  • 10.2.3. An
  • important property of the Hamiltonian
  • 10.3.
  • Integrals of the motion
  • 10.4.
  • Canonical transformations
  • 10.5.
  • Generating functions
  • 10.6.
  • Integrals of motion
  • Transformation solution of Hamiltonians
  • 10.7.
  • Separability
  • 10.7.1. The
  • Hamilton-Jacobi equation
  • 10.7.2.
  • Separable variables
  • Special case - ignorable coordinates
  • 10.8.
  • Constraints in Hamiltonian systems
  • 9.1.
  • 10.9.
  • Time as a coordinate in Hamiltonians
  • Epilogue
  • Index
  • Integrals of the motion
  • 9.2.
  • Jacobi's integral - an energy-like integral
  • 9.3.
  • "Ignorable coordinates" and integrals
Dimensions
24 cm.
Dimensions
unknown
Extent
xix, 540 p.
Form of item
electronic
Isbn
9780387283166
Other physical details
ill.
Reproduction note
Electronic reproduction.
Specific material designation
remote
Stock number
978-0-387-28059-2
System control number
  • 3172498-01okla_normanlaw
  • (SIRSI)3172498
  • (Sirsi) o262691121
  • (OCoLC)262691121

Library Locations

  • Architecture LibraryBorrow it
    Gould Hall 830 Van Vleet Oval Rm. 105, Norman, OK, 73019, US
    35.205706 -97.445050
  • Bizzell Memorial LibraryBorrow it
    401 W. Brooks St., Norman, OK, 73019, US
    35.207487 -97.447906
  • Boorstin CollectionBorrow it
    401 W. Brooks St., Norman, OK, 73019, US
    35.207487 -97.447906
  • Chinese Literature Translation ArchiveBorrow it
    401 W. Brooks St., RM 414, Norman, OK, 73019, US
    35.207487 -97.447906
  • Engineering LibraryBorrow it
    Felgar Hall 865 Asp Avenue, Rm. 222, Norman, OK, 73019, US
    35.205706 -97.445050
  • Fine Arts LibraryBorrow it
    Catlett Music Center 500 West Boyd Street, Rm. 20, Norman, OK, 73019, US
    35.210371 -97.448244
  • Harry W. Bass Business History CollectionBorrow it
    401 W. Brooks St., Rm. 521NW, Norman, OK, 73019, US
    35.207487 -97.447906
  • History of Science CollectionsBorrow it
    401 W. Brooks St., Rm. 521NW, Norman, OK, 73019, US
    35.207487 -97.447906
  • John and Mary Nichols Rare Books and Special CollectionsBorrow it
    401 W. Brooks St., Rm. 509NW, Norman, OK, 73019, US
    35.207487 -97.447906
  • Library Service CenterBorrow it
    2601 Technology Place, Norman, OK, 73019, US
    35.185561 -97.398361
  • Price College Digital LibraryBorrow it
    Adams Hall 102 307 West Brooks St., Norman, OK, 73019, US
    35.210371 -97.448244
  • Western History CollectionsBorrow it
    Monnet Hall 630 Parrington Oval, Rm. 300, Norman, OK, 73019, US
    35.209584 -97.445414
Processing Feedback ...