Herring References

Prof. Robert B. Laughlin
Department of Physics, Stanford University
Stanford, CA 94305

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A11 - Mechanics

Mechanics
	H. Goldstein, Classical Mechanics (Addison-Wesley, 1951).
	V. V. Golubev, Lectures on the Integration of the Equations of Motion of a Rigid Body About a Fixed Point (National Science Foundation, 1953).
	L. I. Sedov, Introduction to the Mechanics of Continuous Media (Addison-Wesley, 1965).
	L. A. Pars, A Treatise on Analytical Dynamics (Wiley, 1965).
	A. A. Andronov, E. A. Leontovich, I. I. Gordon and A. G. Maier, Qualitative Theory of Second-Order Dynamic Systems (Wiley, 1974).
	ibid., Theory of Bifurcations of Dynamical Systems on a Plane (Isreal Program of Sci. Trans., 1971).
	R. H. Abraham and J. E. Marsden, Foundations of Mechanics (Benjamin, 1967).
	B. R. Gossick, Hamilton's Principle and Physical Systems (Academic Press, 1967).
	G. Hamel, Theoretische Mechanik (Springer, 1967).
	A. J. Lichtenberg, Phase Space Dynamics of Particles (Wiley, 1969).
	G. Hamel, Theoretische Mechanik (Springer, 1967).
	C. Lanczos in Mathemical Methods in Solid State and Superfluid Theory, eds. R. C. Clark and G. H. Derrick (Plenum, 1968).
	A. H. Nayfeh Perturbation Methods (Wiley, 1973).
	A. C. Eringen, ed. Continuum Mechanics of Single-Substance Bodies, v. 2 (Princeton, 1975).
	V. I. Arnol'd, Mathematical Methods in Classical Mechanics (Springer, 1978).
	C.-C. Wang Mathematical Principles of Mechanics and Electromagnetism (Plenum, 1979).
	E. A. Desloge Classical Mechanics (Wiley, 1982).
	G. Gallovotti The Elements of Mechanics (Springer, 1983).
	R. S. Mackay and J. D. Meiss Hamiltonian Dynamical Systems (Adam Hilger, 1987).
	A. M. Ozorio de Almeida Hamiltonian Systems: Chaos and Quantization (Cambridge, 1989).
General Formulation of Equations of Motion
	R. Cawley, "Determination of the Hamiltonian in the Presence of Constraints," Phys. Rev. Lett. 42, 413 (1979).
Conservation Laws
	E. L. Hill, "Hamilton's Principle and the Conservation Theorems of Mathematical Physics," Rev. Mod. Phys. 23, 253 (1951).
Variational Methods in Particle Mechanics
	J. M. Luttinger and R. B Thomas Jr., "Variational Method for Studying the Motion of Classical Vibrating Systems," J. Math. Phys. 1, 121 (1960).
	S. T. Epstein, "Hypervirial Method for Studying the Motion of Classical Vibrating Systems," J. Appl. Phys. 33, 235 (1962).
General Theory of Several-Particle Systems
	J. Marsden and A. Weinstein, "Reduction of Symplectic Manifolds with Symmetry," Rep. Math., Phys. 5, 121 (1974).
	J. Moser, "Three Integrable Hamiltonian Systems Connected with Isospectral Deformations," Adv. Math., Phys. 16, 197 (1975).
	F. Calogero, C. Marchioro and O. Ragnisco, "Exact Solution of the Classical and Quantal One-Dimensional Many Body Problems with the Two Body Potential Va(x) = g2a2/sinh2(ax)," Lett. Nuovo Cimento 13, 383 (1975).
	F. Calogero, "Exactly Solvable One-Dimensional Many Body Problems," Lett. Nuovo Cimento 13, 411 (1975).
	F. Calogero, "On a Functional Equation Connected with Integrable Many-Body Problems," Lett. Nuovo Cimento 16, 77 (1975).
	F. T. Smith, "Modified Heliocentric Coordinates for Particle Dynamics," Phys. Rev. Lett. 45, 1157 (1980).
	J. M. Gipson, "Quantum Solution of the Calogero System by the Projection Method," Phys. Rev. Lett. 48, 1511 (1982).
General Theory of Orbits of Hamiltonian Systems
	B. O. Koopman, "Hamiltonian Systems and Transformation in Hilbert Space," Proc. Natl. Acad. Sci. 17, 315 (1931).
	M. Greenspan, "Derivation of the Boltzmann-Ehrenfest Adiabatic Principle," J. Acoustic Soc. Am. 27, 34 (1955).
	P. A. Sturrock, "Action-Transfer and Frequency-Shift Relations in the Nonlinear Theory of Waves and Oscillations," Ann. Phys. (NY) 9, 422 (1960).
	L. M. Garrido, "Approximate Constancy of Adiabatic Invariants," Prog. Theor. Phys. 26, 577 (1961).
	P. A. Sturrock, "Explosive and Nonexplosive Onsets of Instability," Phys. Rev. Lett. 16, 270 (1966).
	P. Bak, "Commensurate Phases, Incommensurate Phases and the Devil's Staircase," Rep. Prog. Phys. 45, 587 (1982).
	A. Ramani, D. Dorizzi and B. Grammaticos, "Painlevé Conjecture Revisited," Phys. Rev. Lett 49, 1539 (1982).
	A. J. Lichtenberg and M. A. Liebermann, Regular and Stochastic Motion, (Springer, 1983).
	F. Cologero in Nonlinear Phenomena, Ed. by K. B. Wolf (Springer, 1983).
	J. Hietarinta et al, "Coupling-constant Metamorphosis and Duality Between Integrable Hamiltonian Systems," Phys. Rev. Lett. 53, 1707 (1984).
	L. S. Hall, "Invariants Polynomial in Momenta for Integrable Hamiltonians," Phys. Rev. Lett. 54, 614 (1985).
	K. M. Case, "Constants of Motion and the Variational Equations," Phys. Rev. Lett. 55, 445 (1985).
	J. L. Tennyson et al., "Change of the Adiabatic Invariant Due to Separatrix Crossing," Phys. Rev. Lett. 56, 2117 (1986).
Miscellaneous General Orbit Theory for Hamiltonian Systems
	J. M. Robbins and R. G. Littlejohn, "Maslov Indices of Resonant Tori," Phys. Rev. Lett. 58, 1388 (1987).
	J. R. Cary and R. T. Skodje, "Reaction Probability for Sequential Separatrix Crossings," Phys. Rev. Lett. 61, 1795 (1988).
	F. Neri and G. Rangarajan, "Kinematic Moment Invariants for Linear Hamiltonian Systems," Phys. Rev. Lett. 64, 1073 (1990).
	R. C. Black and I. I. Satija, "Universal Pattern Underlying the Recurrence of Komogorov-Arnol'd-Moser Tori," Phys. Rev. Lett. 65, 1 (1990).
	M. G. Forest, C. G. Goedde and A. Sinha, "Instability-Driven Energy Transport in Near-Integrable, Many Degrees-of-Freecom, Hamiltonian Systems," Phys. Rev. Lett. 68, 2722 (1992).
	D. J. Evans, "Time Correlation Relation for Lyapunov Exponents," Phys. Rev. Lett. 69, 395 (1992).
	C. Moore, "Braids in Classical Dynamics," Phys. Rev. Lett. 70, 3675 (1993).
Chaotic Orbits of Hamiltonian Systems
	I. I. Satija, "Universal Strange Attractor Underlying Hamiltonian Stochasticity," Phys. Rev. Lett. 58, 623 (1987).
	R. Brown, E. Ott and C. Grebogi, "Ergodic Adiabatic Invariants of Chaotic Systems," Phys. Rev. Lett. 59, 1173 (1987).
	O. Piro and M. Feingold, "Diffusion in Three-Dimensional Liouvillian Maps," Phys. Rev. Lett. 61, 1799 (1988).
	S. Bleher, E. Ott and C. Grebogi, "Routes to Chaotic Scattering," Phys. Rev. Lett. 63, 919 (1989).
	Z. Kovács and T. Tél, "Thermodynamics of Irregular Scattering," Phys. Rev. Lett. 64, 1617 (1990).
Elasticity Theory
	F. D. Murnaghan, Finite Deformation of an Elastic Solid (Wiley, 1951).
	C. Truesdell, The Elements of Continuum Mechanics (Springer, 1966).
	C. Truesdell, ed., Mechanics of Solids II (Springer, 1984).
	R. J. Knops and L. E. Payne, Uniqueness Theorems in Linear Elasticity (Springer, 1971).
	M. Leitman and G. M. C. Fisher, "The Linear Theory of Viscoelasticity," in Handbuch der Physik, v. 6A/3, ed. C. Truesdell (Springer, 1973).
	B. M. Fraeijs de Veubeke, A Course on Elasticity (Springer, 1979).
	P. L. Gould, Introduction to Linear Elasticity (Springer, 1983).
Theory of Finite Strain
	F. D. Murnaghan, "Finite Deformations of an Elastic Solid," Am. J. Math. 59, 235 (1937).
	F. D. Murnaghan, "Foundations of the Theory of Elasticity," Proc. Symp. Appl. Math. 1, 158 (1949).
	F. Birch, "The Effect of Pressure Upon the Elastic Parameters of Isotropic Solids, According to Murnaghan's Theory of Finite Strain," J. Appl. Phys. 9, 279 (1938).
	F. Birch,"Finite Elastic Strain of Cubic Crystals," Phys. Rev. 71, 809 (1947).
	R. Kappus, "Zur Elastizitätstheorie endlicher Verschiebungen," Z. angew. Math. Mech. 19, 271 (1939).
	C. Truesdell, "The Mechanical Foundations of Elasticity and Fluid Dynamics," J. Rational Mech. Anal. 1, 125 (1952).
	C. Truesdell, "Two Measures of Vorticity," J. Rational Mech. Anal. 2, 173 (1953).
	C. Truesdell, "Corrections and Additions to: The Mechanical Foundations of Elasticity and Fluid Dynamics," J. Rational Mech. Anal. 2, 595 (1953).
	M. A. Jaswon and B. J. Shaw, "A Note on Non-Equilbrium Elastic Constants," Proc. Phys. Soc. 77, 885 (1961).
	E. Kröner, "Die neuen Konzeptionen der Kontinuumsmechanik der festen Körper," Phys. Stat. Sol. 1, 3 (1961).
	A. E. Green and J. E. Adkins, Large Elastic Deformations and Non-Linear Continuum Mechanics (Oxford, 1960).
	F. Davies, "Invariant Finite Measures in Elasticity and Lattice Dynamics," J. Phys. Chem. Solids 34, 841 (1973).
Existence Theorems in Elasticity and Anelasticity
	T. Alfrey, "Non-Homogeneous Stresses in Visco-Elastic Media," Quart. Appl. Math. 2, 133 (1944).
	I. C. Arzhanykh, "On the Theory of Integration of the Dynamical Equations of an Isotropic Elastic body," Dokl. Acad. Nauk SSSR 73, 41 (1950).
	R. D. Mindlin, "A Mathematical Theory of Pseudo-Viscoelasticity," J. Appl. Phys. 20, 206 (1945).
	W. T. Read Jr., "Stress Analysis for Compressible Viscoelastic Materials," J. Appl. Phys. 21, 621 (1950).
	A. S. Lodge, "A New Theorem in the Classical Theory of Elasticity," Nature 169, 926 (1952).
Fundamental Equations of Viscoelasticity
	C. M. Vest and V. S. Arpaci, "Overstability of a Viscoelastic Fluid Heated from Below," J. Fluid Mech. 36, 613 (1969).
	M. F. Kanninen et al., eds., Inelastic Behavior of Solids, (McGraw-Hill, 1970).
Hydro- and Aero-Dynamics
	L. M. Milne-Thompson, Theoretical Aerodynamics (Van Nostrand, 1948).
	L. M. Milne-Thompson, Theoretical Hydrodynamics (Macmillan, 1960).
	A. Sommerfeld, Vorlesungen über Theoretische Physik (Deutsche Verlagsbuchhandlung Wiesbaden, 1947).
	H. L. Dryden, F. P. Murnaghan and H. Bateman, Hydrodynamics (Dover, 1956).
	R. J. Seeger and G. Temple, eds., Research Frontiers in Fluid Dynamics (Interscience, 1965).
	N. E. Kochin, I. A. Kibel' and N. V. Roze Theoretical Hydrodynamics (Interscience, 1964).
	C. Truesdell, The Elements of Continuum Mechanics (Springer, 1966).
	S. Eskinaze, Vector Mechanics of Fluids and Magnetofluids (Academic Press, 1967).
	G. K. Batchelor, An Introduction to Fluid Dynamics (Cambridge, 1967).
	M. Holt, ed. , Basic Developments in Fluid Mechanics (Academic Press, 1965).
	C. C. Wang, Mathematical Principles of Mechanics and Electromagnetism, Part A: Analytical and Continuum Mechanics (Plenum, 1979).
	M. Gitterman, "Hydrodynamics of a Fluid Near a Critical Point," Rev. Mod. Phys. 50, 85 (1978).
	B. S. Massey, Mechanics of Fluids (Van Nostrand, 1983).
	M. T. Sprackling, Liquids and Solids (Routledge, 1985).
	S. N. Shore, An Introduction to Astrophysical Hydrodynamics (Academic Press, 1992).
	L. M. Milne-Thompson, Theoretical Aerodynamics (Van Nostrand, 1948).
Fundamental Equations of Hydrodynamics
	L. Tisza, "Supersonic Absorption and Stokes' Viscosity Relation," Phys. Rev. 61, 531 (1942).
	C. Eckart, "Vortices and Streams Caused by Sound Waves," Phys. Rev. 73, 68 (1948).
	C. Eckart, "The Thermodynamics and Irreversible Processes IV: The Theory of Elasticity and Anelasticity," Phys. Rev. 73, 373 (1948).
	C. Eckart, "The Theory of the Anelastic Fluid," Rev. Mod. Phys. 20, 232 (1948).
	M. M. Munk and R. C. Prim, "On the Canonical Form of the Equations of Steady Motion of a Perfect Gas," J. App. Phys. 19, 957 (1948).
	F. E. Fox and K. F. Herzfeld, "On the Forces Producing the Ultrasonic Wind," Phys. Rev. 78, 156 (1950).
	C. Truesdell, "On the Mechanical Foundations of Elasticity and Fluid Dynamics," J. Rat. Mech. Anal. 1, 125 (1952).
	J. J. Markham, "Second-Order Acoustic Fields: Streaming with Viscosity and Relaxation," Phys. Rev. 86, 497 (1952).
	R. Zelazney, "Derivation of Hydrodynamic Equations for the Quantum Systems of Diatomic Molecules," Phys. Rev. 117, 1 (1960).
	S. Chapman and J. G. Cowling, The Mathematics of Non-Thermal Gases (Cambridge, 1970).
	P. J. Morrison and J. M. Greene, "Noncanonical Hamilton Density formulation of Hydrodynamics and Ideal Magnetohydrodynamics," Phys. Rev. Lett. 45, 790 (1980).
	R. J. Becker, "Lagrangian/Hamiltonian Formalism for Description of Navier-Stokes Fluids," Phys. Rev. Lett. 58, 1419 (1986).
	P. Garbaczweski and G. Kondrat, "Burgers Velocity Fields and Dynamical Transport Processes," Phys. Rev. Lett. 77, 2608 (1996).
General Integrals of the Hydrodynamic Equations
	C. Truesdell, "Bernoullis's Theorem for Viscous Compressible Fluids," Phys. Rev. 77, 535 (1950).
	C. Etkin and V. G. Szebekely, "Comment on Truesdell's Paper on Bernoullis's Theorem for Viscous Compressible Fluids," Phys. Rev. 80, 767 (1950).
	J. J. Van Deemter, "Bernoulis's Theorem for Viscous Fluids," Phys. Rev. 85, 1049 (1952).
Integral Theorems in Hydrodynamics
	C. Truesdell, "On the Total Vorticity of Motion of a Continuous Medium," Phys. Rev. 73, 510 (1948).
	C. Truesdell, "On the Transfer of Energy in Continuous Media," Phys. Rev. 73, 513 (1948).
	E. R. Huggins, "Exact Magnus-Force Formula for Three-Dimensional Fluid-Core Motion," Phys. Rev. A 1, 327 (1970).
	E. R. Huggins, "Energy-Dissipation Theorem and Detailed Josephson Equation for Ideal Incompressible Fluids," Phys. Rev. A 1, 332 (1970).
	R. H. Kraichman, J. Fluid Mech. 67, 155 (1975).
	M. A. Virasoro, "Variational Principle for Two-Dimensional Incompressible Hydrodynamics and Quasigeostrophic Flows," Phys. Rev. Lett 47, 118 (1981).
General Aspects of Hydrodynamic Stability
	M. Lee et al., "Long Wavelength Instability for Uniform Shear Flow," Phys. Rev. Lett. 76, 2702 (1996).
Diabatic Flow
	B. L. Hicks, "An Extension of the Theory of Diabatic Flow," Phys. Rev. 77, 286 (1950).
	B. L. Hicks, "Diabatic Flow of a Compressible Fluid," Quart. Appl. Math. 6, 221 (1948).
	B. L. Hicks, "On the Characterization of Fields of Diabatic Flow," Quart. Appl. Math. 6, 407 (1948).
	V. P. Starr, "A Mathematical Theory of Convection," J. Meteor. 6, 188 (1949).
	G. P. Zank and W. H. Matthaeus, "Nearly Incompressible Hydrodynamics and Heat Conduction," Phys. Rev. Lett. 64, 1243 (1990).
Acoustics
	D. I. Blokhintsev, Acoustics of a Nonhomogeneous Moving Medium (Gostechizdat, Moscow-Leningrad, 1946).
	W. P. Mason, ed., Physical Acoustics (Academic Press, 1965).
	P. M. Morse and K. U. Ingard, Theoretical Acoustics (McGraw-Hill, 1968).
	P. D. Edmonds, ed., Ultrasonics, Methods in Experimental Physics, vol. 19 (Academic Press, 1981).
Fundamental Equations of Acoustics
	P. G. Bergmann, "The Wave Equation in a Medium with a Variable Index of Refraction," J. Acoustic Soc. Am. 17, 329 (1946).
	D. Blokhintzev, "The Propagation of Sound in an Inhomogeneous and Moving Medium," J. Acoustic Soc. Am. 18, 322 (1946).
	C. Eckart, "Vortices and Streams Caused by Sound Waves," Phys. Rev. 73, 68 (1948).
	J. R. Pellam, "Wave Transmission and Reflection Phenomena in Liquid Helium II," Phys. Rev. 73, 608 (1948).
	F. E. Fox and K. F. Herzfeld, "On the Forces Producing the Ultrasonic Wind," Phys. Rev. 78, 156 (1950).
	J. J. Markham, "Second-Order Acoustic Fields: Streaming with Viscosity and Relaxation," Phys. Rev. 86, 497 (1952).
	J. J. Markham, "Second-Order Acoustic Fields: Relation Between Density and Pressure," Phys. Rev. 86, 710 (1952).
	J. J. Markham, "Second-Order Acoustic Fields: Energy Relations," Phys. Rev. 86, 712 (1952).
	J. J. Markham, "Second-Order Acoustic Fields: Relation Between Energy and Intensity," Phys. Rev. 89, 972 (1953).
	F. Borgnis, "On the Physics of Acoustic Radiation Pressure," Z. Phys. 134, 363 (1953).
	P. E. Doak, "Vorticity Generated by Sound," Proc. Roy. Soc. 226, 7 (1954).
	J. E. Piercy and J. Lamb, "Acoustic Streaming in Liquids," Proc. Roy. Soc. 226, 43 (1954).
	J. Meixner, "On the Thermodynamic Theory of the Second Viscosity," Proc. Roy. Soc. 226, 51 (1954).
	L. Tisza, "Supersonic Absorption and Stokes' Viscosity Relation," Phys. Rev. 61, 531 (1954).
	J. G. Oldroyd, "Note on the Hydrodynamic and Thermodynamic Pressures," Proc. Roy. Soc. 226, 57 (1954).
	G. Truesdell, "The Present Status of the Controversy Regarding the Bulk Viscosity of Fluids," Proc. Roy. Soc. 226, 59 (1954).
	M. J. P. Musgrave, "On the Propagation of Elastic Waves in Aelotropic Media," Proc. Roy. Soc. 226, 339 (1954).
	J. Awatani, "Studies of Acoustic Radiation Pressure," J. Acoustic Soc. Am. 27, 278 (1955).
	F. V. Hunt, "Notes on the Exact Equations Governing the Propagation of Sound in Fluids," J. Acoustic Soc. Am. 27, 1019 (1955).
	E. J. Post, "Meaning and Interpretation of Acoustic Momentum and Acoustic Radiation Stress," Phys. Rev. 118, 1113 (1960).
	P. A. Sturrock, "Energy-Momentum Tensor for Plane Waves," Phys. Rev. 121, 18 (1961).
	P. A. Sturrock, "In What Sense Do Slow Waves Carry Momentum and Energy?" J. Appl. Phys. 31, 2052 (1960).
	J. R. Pierce, "Momentum and Energy of Waves," J. Appl. Phys. 32, 2580 (1961).
	P. M. Morse and H. Feshbach, Methods of Theoretical Physics, (McGraw-Hill, 1953), pp 318-24.
	I. H. Gilbert and B. R. Mollow, "Momentum of Longitudinal Elastic Vibrations," Am. J. Phys. 36, 822 (1968).
	W. H. Nichols and E. F. Carome, "Light Scattering from a Multiply Relaxing fluid," J. Chem. Phys. 49, 1000 (1968).
Collective Motions
	Y. Watanabe, "A Classical Theory of the Collective Description," Prog. Theor. Phys. 16, 1 (1956).
	L. Friedland, G. Goldner and A. N. Kaufman, "Four-Dimensional Eikonal Theory of Linear Mode Conversion," Phys. Rev. Lett. 58, 1392 (1987).
Vibrations of Special Systems
	R. J. Rubin and R. Zwanzig, "A Lattice with an Unusual Frequency Spectrum," J. Math. Phys. 2, 861 (1961).
Scattering of Sound by Sound
	P. J. Westervelt, "Scattering of Sound by Sound," J. Acoustic Soc. Am. 29, 199 (1957).
	P. J. Westervelt, "Scattering of Sound by Sound," J. Acoustic Soc. Am., 934 (1957).
	V. R. Lauvstad and S. Tøtta, "Problem of Sound Scattering by Sound," J. Acoustic Soc. Am 34, 1045 (1962).
	A. L. Thuras, R. T. Jenkins and H. T. O'Neil, "Extraneous Frequencies Generated in Air Carrying Intense Sound Waves," J. Acoustic Soc. Am 6, 173 (1935).
	L. W. Dean III, "Interaction Between Sound Waves," J. Acoustic Soc. Am 34, 1039 (1962).
	V. R. Lauvstad, "Nonlinear Interaction of Two Monochromatic Soundwaves," Acustica 16, 191 (1965).
	C. S. Tsai, "Scattering of Acoustic Waves from a Moving Elastic Nonlinearity," J. Acoustic Soc. Am 44, 458 (1968).
	J. P. Jones and R. T. Beyer, "Scattering of Sound by Sound," J. Acoustic Soc. Am 48, 398 (1970).
	V. A. Zverev and A. I. Kalachev, "Modulation of Sound by Sound in Interaction of Sound Waves," Sov. Phys. Acoust. 16, 204 (1970).
	J. M Rouvaen, E. Bridoux and R. Torguet, "Scattering of Sound by Sound in Solids," Appl. Phys. Lett. 22, 619 (1973).
	J. L. S. Bellin and R. T. Beyer, "Experimental Investigation of an End-Fire Array," J. Acoustic Soc. Am 34, 1051 (1962).
Scattering of Sound by Miscellaneous Disturbances
	N. I. Pushkina and R. V. Khokholov, "Temperature Scattering of Sound in a Solid," Zh. Eksp. Teor. Fiz. 57, 1263 (1969) [Sov. Phys. JETP 30, 687 (1970)].
General Theory of Scattering
	Y. N. Demkov, "Virial Theorem and its Generalizations in Scattering Theory," Dokl. Akad. Nauk SSSR 138, 86 (1961) [Sov. Phys. Doklady 6, 393 (1961)].
Theory of Dissipative Systems
	A. A. Andronov, E. A. Leontovich, I. I. Gordon and A. G. Maier, Qualitative Theory of 2nd Order Dynamic Systems," (Halsted Press, 1973).
	M. A. Lieberman and K. Y. Tsang, "Transient Chaos in Dissipatively Perturbed, Near-Integrable Hamiltonian Systems," Phys. Rev. Lett. 55, 908 (1985).