Intermediate dynamics : a linear algebraic approach /

Bibliographic Details
Main Author:	Howland, R. A., 1943-
Corporate Author:	SpringerLink (Online service)
Format:	eBook
Language:	English
Published:	New York : Springer, [2006]
Series:	Mechanical engineering series (Berlin, Germany)
Subjects:	Algebras, Linear. Dynamics. Electronic books.
Online Access:	Connect to the full text of this electronic book Publisher description

Table of Contents:

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