http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
3. Special case - square matrices -- The "algebra" of square matrices -- 3.1. The inverse of a square matrix -- Properties of the inverse -- 3.2. The 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 -- 3.5. 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 -- 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. Linearly independent eigenvectors - diagonalization -- Diagonalization of real symmetric matrices -- 3.7.2. Linearly dependent eigenvectors - Jordan normal form --
5. Kinetics -- 5.1. Particles and systems of particles -- 5.1.1. Particle kinetics -- Linear momentum and its equation of motion -- Angular momentum and its equation of motion -- 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. 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 -- 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 -- Work -- Energy principles -- 5.4.2. Momentum - - 5.4.3 Conservation application in general -- Epilogue --
9. Integrals of motion -- 9.1. Integrals of the motion -- 9.2. Jacobi's integral - an energy-like integral -- 9.3. "Ignorable coordinates" and integrals -- 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. 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. 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 -- 10.9. Time as a coordinate in Hamiltonians -- Epilogue -- Index.
[pt]. 2. 3-D rigid body dynamics -- Prologue -- 4. Kinematics -- 4.1. Motion of a rigid body -- 4.1.1. 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. 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. 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. 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. 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 --
[pt]. 3. Analytical dynamics -- Prologue -- 6. Analytical dynamics : perspective -- 6.1. Vector formulations and constraints -- 6.2. 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. 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 -- 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 -- Interpretation of the Lagrange multipliers -- 8.4. Time as a coordinate --
Preface -- [pt]. 1. Linear algebra -- Prologue -- 1. Vector spaces -- 1.1. Vectors -- 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 -- 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. 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. 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 -- 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 -- Homogeneous linear equations -- Non-homogeneous linear equations -- 2.4. Linear operators - differential equations --
Electronic reproduction. New York : Springer, 2008. Mode of access: World Wide Web. System requirements: Web browser. Title from title screen (viewed on Oct. 10, 2008). Access may be restricted to users at subscribing institutions.
Includes bibliographical references and index.
Mechanical engineering series (Berlin, Germany)