Matrix methods for engineering:
Saved in:
| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Englewood Cliffs, N.J.
Prentice-Hall
1963
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Prentice-Hall international series in applied mathematics. |
| Physical Description: | XIII, 427 S. |
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MARC
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| 100 | 1 | |a Pipes, Louis Albert |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Matrix methods for engineering |
| 264 | 1 | |a Englewood Cliffs, N.J. |b Prentice-Hall |c 1963 | |
| 300 | |a XIII, 427 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Prentice-Hall international series in applied mathematics. | ||
| 650 | 4 | |a Mathématiques de l'ingénieur | |
| 650 | 4 | |a Matrices | |
| 650 | 4 | |a Engineering mathematics | |
| 650 | 4 | |a Matrices | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005987178&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-005987178 | ||
Record in the Search Index
| _version_ | 1804123402069344256 |
|---|---|
| adam_text | TABLE OF CONTENTS
INTRODUCTION, I
1THE ELEMENTS OF
THE THEORY OF DETERMINANTS, 3
1. Introduction, 3.
2. Fundamental definitions and notation, 3.
3. Minors and cofactors, 4.
4. The Laplace expansion of a determinant, 5.
5. Fundamental properties of determinants, 7.
6. The expansion of numerical determinants, 8.
7. The method of pivotal condensation, 10.
8. The solution of linear equations. Cramer s rule, 13.
9. Multiplication and differentiation of determinants, 15.
2 THE FUNDAMENTALS
OF MATRIX ALGEBRA, 18
1. Introduction, 18.
2. Definition of a matrix, 18.
3. Principal types of matrices, 19.
4. Equality of matrices, addition and subtraction, 20.
5. Multiplication of matrices, 21.
6. Matrix division, the inverse matrix, 24.
7. Matrix division, 28.
8. The reversal law in transposed and reciprocal products, 29.
9. Diagonal matrices and their properties, 31.
10. Partitioned matrices and partitioned multiplication, 31.
11. Matrices of special types, 32.
12. The solution of n linear equations in n unknowns, 34.
vii
Viii TABLE OF CONTENTS
3 MATRICES AND
EIGENVALUE PROBLEMS, 38
1. Introduction, 38.
2. The eigenvalues of a square matrix, 38.
3. Geometrical interpretation of the eigenvalue problem, 40.
4. Invariants of the rotated matrix [M]r, 45.
5. Algebraic discussion of the eigenvectors of a matrix, 46.
6. The eigenvalues of a real symmetric matrix are real numbers,
49.
7. Hermitian matrices, 50.
8. Orthogonal transformations, 51.
9. Symmetric matrices and quadratic forms, 53.
10. The transformation of a quadratic form into a sum of squares
by means of an orthogonal transformation, 54.
11. Commutative matrices, 57.
12. Fundamental properties of the characteristic determinant and
the characteristic equation of a matrix, 59.
4 THE CALCULUS
OF MATRICES, 65
1. Introduction, 65.
2. Matrix polynomials, 65.
3. Infinite series of matrices, 66.
4. The convergence of series of matrices, 67.
5. The matric exponential function, 69.
6. The matric trigonometric and hyperbolic functions, 70.
7. The matric binomial theorem (commutative matrices), 72.
8. The Cayley Hamilton theorem, 73.
9. Reduction of polynomials by the Cayley Hamilton theorem, 75.
10. The inversion of a matrix by the use of the Cayley Hamilton
theorem, 77.
11. Functions of matrices and Sylvester s theorem, 78.
12. Applications of Sylvester s theorem, 82.
13. The use of the characteristic equation in evaluating functions
of matrices, 83.
14. Differentiation and integration of matrices, 88.
15. Association of matrices with linear differential equations, 90.
16. The solution of difference equations by the use of matrices, 94.
TABLE OF CONTENTS ix
5 MATRIX METHODS IN
THE THEORY OF ELASTICITY, 100
1. Introduction, 100.
2. Stress. Definition and notation, 100.
3. Stresses in two dimensions, 102.
4. Stresses in three dimensions, 106.
5. Infinitesimal strain in three dimensions, 111.
6. The strain energy of the medium, 117.
7. The stress strain relations for an elastic isotropic solid, 117.
8. The principal elastic constants, 120.
9. The strain expressed in terms of the stress, 122.
10. The elastic equations of motion, 122.
11. The elastic equations of equilibrium, 125.
12. The stresses on a semi infinite solid strained by gravitational
forces, 126.
6 MATRIX METHODS IN
THE ANALYSIS OF STRUCTURES, 129
1. Introduction, 129.
2. The flexibility and stiffness matrices, 130.
3. Conservative bodies and the strain energy, 134.
4. Castigliano s theorem, 135.
5. The principal directions of loading at a point of an elastic
body, 135.
b. The principle of minimum potential energy, 136.
7. Determination of the flexibility matrix of a complex structure,
137.
8. The force method of stress analysis, 138.
9. The modified flexibility matrix, 142.
10. Analysis of modified structures, 144.
11. Modifications of the elements of the structure, 147.
12. The flexibility of the modified structure, 150.
13. The displacement method of stress analysis, 151.
14. The effect of the application of initial stresses p0 with the con¬
straint S=0, 154.
15. Analysis of modifications of the structure, 155.
16. The stiffness matrix of the modified structure, 157.
17. Special types of modification of the structure, 157.
X TABLE OF CONTENTS
7 APPLICATIONS OF MATRICES
TO CLASSICAL MECHANICS, 163
1. Introduction, 163.
2. The matrix representation of a vector product, 163.
3. Rotation of rectangular axes, 165.
4. Kinematics and angular velocity, 166.
5. Change of reference axes in two dimensions, 170.
6. Successive rotations, 172.
7. Angular coordinates of a three dimensional reference frame,
172.
8. The transformation matrix [L] and instantaneous angular ve¬
locities expressed in angular coordinates, 174.
9. The components of velocity and acceleration, 175.
10. The kinetic energy of a rigid body, 177.
11. Principal axes and the moments of inertia, 179.
12. Transformation of forces and couples, 181.
13. The equations of motion of a rigid body, 183.
14. Transformation of the equation of motion to moving axes, 186.
15. General form of Euler s equations, 189.
16. Motion relative to the surface of the earth, 193.
17. The plumb line, 196.
18. Motion of a free particle near the surface of the rotating
earth, 198.
19. The Foucault pendulum ,201.
20. The motion of atop, 203.
8 APPLICATIONS OF MATRICES
TO VIBRATION PROBLEMS, 210
1. Introduction, 210.
2. Transformation of coordinates, 210.
3. Lagrange s equations of motion, 212.
4. Electrical and mechanical analogies, 214.
5. Systems having two degrees of freedom (conservative case),
218.
6. The general case: mass weighted coordinates, 224.
7. The vibration of conservative systems with dynamic coupling,
227.
TABLE OF CONTENTS xi
8 APPLICATIONS OF MATRICES
TO VIBRATION PROBLEMS (Cont d)
8. Fundamental properties of the modal matrix [A], 231.
9. The case of three coupled pendulums, 234.
10. The case of zero frequency, 238.
11. The use of functions of matrices in the theory of vibrations,
241.
12. Use of functions of matrices in the case of dynamic coupling,
247.
13. The case of multiple roots of the characteristic equation, 249.
14. The oscillations of a symmetric electric circuit, 251.
15. Nonconservative systems. Vibrations with viscous damping,
254.
16. The motion of a general damped linear dynamic system, 256.
17. The use of matrix iteration to determine the frequencies and
modes of oscillation of linear conservative systems, 262.
18. Numerical example, 264.
19. Determination of the higher modes: the sweeping matrix, 267.
20. A numerical example of the iteration procedure, 270.
21. The analysis of a class of symmetric damped linear systems,
279.
22. The Routh Hurwitz stability criterion, 282.
23. The location of the eigenvalues of a matrix, 285.
9 THE STEADY STATE SOLUTION OF
THE GENERAL n MESH CIRCUIT, 288
1. Introduction, 288.
2. The general network, 288.
3. Formulation of the problem in terms of mesh currents, 290
4. The canonical equations and their solution, 292.
5. Steady state solution, one applied sinusoidal electromotive
force, 295.
6. Case of n sinusoidal electromotive forces of different phases,
298.
7. Voltages of different frequencies simultaneously impressed,
298.
xii TABLE OF CONTENTS
WTHE TRANSIENT SOLUTION
OF THE GENERAL NETWORK, 305
1. Introduction, 305.
2. The heuristic process, 305.
3. The determinantal equation, 306.
4. The normal modes, 306.
5. The modal matrix, 307.
6. The relation between the amplitudes, 307.
7. Determination of the arbitrary constants, 308.
8. The case of repeated roots of the determinantal equation,
311.
9. The energy functions of the general network, 313.
UTHE DISSIPATIOHLESS
NETWORK, 316
1. Introduction, 316.
2. The canonical equations and the steady state solution, 316.
3. The transient solution, 319.
4. Determination of the fundamental frequency, 322.
5. Completion of the solution, 323.
6. Evaluation of the arbitrary constants, 325.
7. Normal coordinates, 326.
8. Illustrative example, 327.
9. Effect of small resistance terms, 333.
10. The potential function, 334.
11. Computation of the attenuation constants, 336.
m 0) THE STEADY STATE ANALYSIS
JLZl OF FOUR TERMINAL NETWORKS, 337
1. Introduction, 337.
2. The general equations, 337.
3. Alternative form of the equations, 340.
4. Interconnection of four terminal networks, 341.
5. The chain matrices of common structures, 347.
6. The homographic transformation, 351.
7. Cascade connection of dissymmetrical networks, 352.
8. Attenuation and pass bands, 359.
9. The smooth transmission lines, 361.
10. The general ladder network, 363.
TABLE OF CONTENTS xiii
n STEADY STATE SOLUTION
OF MULTICONDUCTOR LINES, 365
1. Introduction, 365.
2. The coefficients of capacity and induction, 366.
3. The electromagnetic coefficients, 367.
4. The general differential equations, 368.
5. The steady state equations, 370.
6. Solution of the equations, boundary conditions, 371.
7. The determinantal equation, 375.
8. Transformation of the basic equations, 378.
9. Solution in terms of terminal impedances, 381.
10. General considerations, 383.
% A TRANSIENT ANALYSIS
!*¦ OF MULTICONDUCTOR LINES, 384
1. Introduction, 384.
2. The general equations, 384.
3. The dissipationless case, 386.
4. The general case, 390.
5. The case of ring symmetry, 392.
6. General boundary conditions, 395.
7. General considerations, 397.
APPENDIX
1THE ELEMENTS OF THE
THEORY OF LAPLACE TRANSFORMS, 401
APPENDIX
2 THE BASIC THEOREMS OF
THE LAPLACE TRANSFORMS, 404
APPENDIX
3 TABLE OF
BASIC TRANSFORMS, 407
INDEX, 425
|
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| spelling | Pipes, Louis Albert Verfasser aut Matrix methods for engineering Englewood Cliffs, N.J. Prentice-Hall 1963 XIII, 427 S. txt rdacontent n rdamedia nc rdacarrier Prentice-Hall international series in applied mathematics. Mathématiques de l'ingénieur Matrices Engineering mathematics HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005987178&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pipes, Louis Albert Matrix methods for engineering Mathématiques de l'ingénieur Matrices Engineering mathematics |
| title | Matrix methods for engineering |
| title_auth | Matrix methods for engineering |
| title_exact_search | Matrix methods for engineering |
| title_full | Matrix methods for engineering |
| title_fullStr | Matrix methods for engineering |
| title_full_unstemmed | Matrix methods for engineering |
| title_short | Matrix methods for engineering |
| title_sort | matrix methods for engineering |
| topic | Mathématiques de l'ingénieur Matrices Engineering mathematics |
| topic_facet | Mathématiques de l'ingénieur Matrices Engineering mathematics |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005987178&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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