Dynamics of Physical Systems

by Cannon, Robert H., Jr.

• ISBN13: 9780486428659
• ISBN10: 0486428656
• Format: Paperback
• Copyright: 2003-09-16
• Publisher: Dover Publications

Summary

Comprehensive text and reference covers modeling of physical systems in several media, derivation of differential equations of motion and related physical behavior, dynamic stability and natural behavior, response to continuing and abrupt forcing inputs, and analysis and synthesis of feedback control systems. 334 figures. 12 tables. 1967 edition.

Table of Contents

Dynamic Investigation	1	(30)
The scope of dynamic investigation	3	(1)
The stages of a dynamic investigation	4	(4)
The block diagram: a conceptual tool	8	(2)
Stage I. Physical modeling: from actual system to physical model	10	(9)
Dimensions and units	19	(12)
PART A: EQUATIONS OF MOTION FOR PHYSICAL SYSTEMS
Equations of Motion for Simple Physical Systems: Mechanical, Electrical, and Electromechanical	31	(63)
Stage II. Equations of motion: from physical model to mathematical model	32	(2)
One-dimensional mechanical systems	34	(19)
Mechanical energy and power	53	(1)
Gear trains and levers	54	(3)
Motion in two and three dimensions	57	(1)
Simple electrical systems	57	(17)
A recapitulation of Procedure A	74	(1)
Amplifiers and transformers	75	(4)
Simple electromechanical systems	79	(6)
Electromechanical elements: an empirical sampling	85	(9)
Equations of Motion for Simple Heat-Conduction and Fluid Systems	94	(27)
Simple heat conduction	94	(8)
Simple fluid systems	102	(19)
Analogies	121	(22)
Analogies between physical media	121	(4)
The electrical analog of mechanical systems	125	(7)
Classification of dynamic system elements	132	(1)
The benefits and limitations of analysis by analog	133	(4)
The network approach to analysis	137	(6)
Equations of Motion for Mechanical Systems in Two and Three Dimensions	143	(39)
Geometry of motion in two and three dimensions	143	(6)
Rotating reference frames	149	(3)
Dynamic equilibrium for rigid body in general motion	152	(4)
Equations of motion for systems of rigid bodies: examples	156	(3)
Advantages of the D'Alembert method. The gyro	159	(4)
Energy methods	163	(4)
Lagrange's method	167	(2)
Lagrange's method for conservative systems	169	(4)
Lagrange's method for nonconservative systems	173	(5)
The relative advantages of Lagrange's method	178	(2)
PART B: DYNAMIC RESPONSE OF ELEMENTARY SYSTEMS
Introduction	180	(2)
First-Order Systems	182	(43)
First-order systems	183	(3)
Natural (unforced) motion	186	(7)
Forced motion	193	(4)
Linearity and superposition	197	(3)
Initial conditions	200	(4)
Special case: the pure integrator	204	(3)
Special case: resonance	207	(3)
Response to a very short impulse	210	(8)
Initial conditions involving sudden change	218	(2)
Generalization to an arbitrary input: convolution	220	(5)
Undamped Second-Order Systems: Free Vibrations	225	(19)
Physical vibrations	226	(10)
Complex numbers	236	(2)
Mathematical operations with complex numbers	238	(4)
Complex-vector (phasor) representation of a sine wave	242	(2)
Damped Second-Order Systems	244	(65)
Second-order systems	245	(1)
Natural motion	246	(2)
Dynamic characteristics and the s plane	248	(7)
Initial conditions: 1 < ζ	255	(2)
Initial conditions: ζ < 1	257	(2)
Sketching time response when ζ < 1	259	(4)
Initial conditions: ζ = 1	263	(3)
Forced motion alone	266	(7)
Transfer functions and pole-zero diagrams	273	(7)
Impedance and admittance	280	(2)
Total response to abrupt disturbances	282	(8)
Transient and steady state	290	(1)
Impulse response of certain second-order systems	291	(7)
Response of a second-order system by convolution	298	(1)
Simulation: the analog computer	299	(10)
Forced Oscillations of Elementary Systems	309	(46)
The nature of sinusoidal response	311	(2)
Operation at a single frequency: the impedance viewpoint	313	(1)
Frequency response	314	(7)
Computing frequency response	321	(1)
Logarithmic scales for plotting frequency response	322	(2)
Forced oscillation of first-order systems: the plotting techniques of Bode	324	(6)
Forced oscillation of undamped second-order systems: resonance	330	(5)
Forced oscillation of damped second-order systems	335	(2)
Techniques for plotting second-order frequency response	337	(5)
Obtaining frequency response from the s plane	342	(3)
Seismic instruments	345	(7)
Frequency response of RLC circuits	352	(3)
Natural Motions of Nonlinear Systems and Time-Varying Systems	355	(21)
Methods of linear approximation	356	(4)
State-space analysis	360	(7)
Large motions of pendulum with damping	367	(2)
Piecewise-linear elements	369	(1)
Linear equations with time-varying coefficients	370	(4)
PART C: NATURAL BEHAVIOR OF COMPOUND SYSTEMS
Introduction	374	(2)
Dynamic Stability	376	(43)
The concept of stability	377	(2)
The elementary second-order system	379	(5)
Locus of roots by graphical construction	384	(2)
Damping as a variable	386	(6)
Coupled pairs of first-order systems	392	(1)
Feedback systems	393	(3)
Third-order systems	396	(5)
The root-locus method of Evans	401	(3)
An introduction to root-locus sketching	404	(2)
The method of Routh: third-order example	406	(3)
Routh's method: general case	409	(6)
Special case of a zero term in the first column	415	(1)
Special case of a zero row	416	(3)
Coupled Modes of Natural Motion: Two Degrees of Freedom	419	(38)
Forms of physical coupling	420	(3)
Coupled equations of motion	423	(3)
A simple vibrating system of coupled members	426	(5)
The effect of coupling strength	431	(6)
Beat generation	437	(5)
Inertial coupling	442	(3)
Normal coordinates	445	(2)
General case, with damping: eigenvalues and eigenvectors	447	(10)
Coupled Modes of Natural Motion: Many Degrees of Freedom	457	(35)
Many degrees of freedom	458	(4)
Distributed-parameter systems: equations of motion	462	(5)
Natural motions of a class of one-dimensional distributed-parameter systems	467	(5)
Brief description of general distributed-parameter systems	472	(3)
Certain musical instruments	475	(5)
A note on the musical scale	480	(2)
Rayleigh's method	482	(8)
PART D: TOTAL RESPONSE OF COMPOUND SYSTEMS
Introduction	490	(2)
est and Transfer Functions	492	(18)
Review of the transfer-function concept	493	(2)
Transferred response of subsystems in cascade	495	(2)
Graphical evaluation of transfer functions from the system pole-zero diagram	497	(3)
Transferred response of systems with general coupling	500	(2)
Matrix representation and standard form	502	(7)
Matrix description of eigenvector calculation	509	(1)
Forced Oscillations of Compound Systems	510	(19)
Frequency response of subsystems in cascade	511	(3)
Frequency response of systems with two-way coupling	514	(4)
Resonance in coupled systems	518	(7)
Design for a single frequency: the vibration absorber	525	(4)
Response to Periodic Functions: Fourier Analysis	529	(6)
Real Fourier series	529	(4)
Complex Fourier series	533	(1)
Spectral representation	534	(1)
The Laplace Transform Method	535	(49)
Demonstration of the Laplace transform method	537	(7)
Evolution of the Laplace transform	544	(5)
Application of the Laplace transform: the one-sided Laplace transform	549	(5)
Summary of basic Laplace transform relations	554	(1)
Derivation of common Laplace transform pairs	555	(4)
Transfer functions from Laplace transformation	559	(3)
Total response by the Laplace transform method	562	(5)
The final-value theorem and the initial-value theorem	567	(5)
A system's response to an impulse and its L transform	572	(1)
Initial conditions and impulse response: a physical interpretation	572	(4)
Equations of motion in standard form: state variables	576	(4)
Convolution and the Laplace transform	580	(4)
From Laplace Transform to Time Response by Partial Fraction Expansion	584	(13)
Formulation of the task	584	(1)
Partial fraction expansion: case one	585	(3)
Special handling of complex conjugate poles	588	(1)
Use of the s-plane pole-zero array to compute response coefficients	589	(3)
The case of repeated poles: case two	592	(3)
Summary of Procedure D-2: partial fraction expansion	595	(2)
Complete System Analysis: Some Case Studies	597	(33)
A fluid clutch	600	(5)
An electromechanical shaker	605	(5)
A thermal quenching operation	610	(4)
An aircraft hydraulic servo	614	(3)
The two-axis gyroscope	617	(11)
PART E: FUNDAMENTALS OF CONTROL-SYSTEM ANALYSIS
Introduction	628	(2)
Feedback Control	630	(14)
The philosophy of feedback control	631	(4)
Performance objectives	635	(2)
The sequence of control-system analysis	637	(1)
Review of dynamic coupling	638	(1)
The algebra of loop closing	639	(5)
Evans' Root-Locus Method	644	(39)
The basic principle	645	(6)
Root-locus sketching procedure	651	(2)
Sketching rules for 180° loci	653	(2)
Rule 1: Real-axis segments	655	(2)
Rule 2: Asymptotes	657	(3)
Rule 3: Directions of departure and arrival	660	(4)
Rule 4: Breakaway from the real axis	664	(5)
Rule 4 (continued): The saddle-point concept	669	(4)
Rule 5: Routh and Evans	673	(4)
Rule 6: Fixed centroid	677	(1)
A typical construction of root loci	678	(4)
Summary	682	(1)
Some Case Studies in Automatic Control	683	(74)
Analysis of an electromechanical remote-indicator servo	683	(8)
Synthesis of indicator servo using network compensation to improve performance	691	(5)
Roll-control autopilot: a multiloop system	696	(7)
Control of an unstable mechanical system: the stick balancer	703	(8)
APPENDICES
A Physical conversion factors to eight significant figures	711	(1)
B Vector dot product and cross product	712	(2)
C Vector differentiation in a rotating reference frame	714	(2)
D Newton's laws of motion	716	(2)
E Angular momentum and its rate of change for a rigid body; moments of inertia	718	(3)
F Fluid friction for flow through long tubes and pipes	721	(2)
G Duals of electrical networks	723	(2)
H Determinants and Cramer's rule	725	(2)
I Computation with a Spirule	727	(4)
J Table of Laplace transform pairs	731	(26)
Problems	757	(108)
Answers to odd-numbered problems	865	(16)
Selected references	881	(4)
Index	885	(20)
About the Author	905