Showing papers on "Equations of motion published in 2007"

One path to acoustic cloaking

Abstract: A complete analysis of coordinate transformations in elastic media by Milton et al has shown that, in general, the equations of motion are not form invariant and thus do not admit transformation-type solutions of the type discovered by Pendry et al for electromagnetics. However, in a two-dimensional (2D) geometry, the acoustic equations in a fluid are identical in form to the single polarization Maxwell equations via a variable exchange that also preserves boundary conditions. We confirm the existence of transformation-type solutions for the 2D acoustic equations with anisotropic mass via time harmonic simulations of acoustic cloaking. We discuss the possibilities of experimentally demonstrating acoustic cloaking and analyse why this special equivalence of acoustics and electromagnetics occurs only in 2D.

Extra force in f(R) modified theories of gravity

Abstract: The equation of motion for massive particles in f(R) modified theories of gravity is derived. By considering an explicit coupling between an arbitrary function of the scalar curvature, R, and the Lagrangian density of matter, it is shown that an extra force arises. This extra force is orthogonal to the four-velocity and the corresponding acceleration law is obtained in the weak-field limit. Connections with MOND and with the Pioneer anomaly are further discussed.

Gravitational Wave Spectrum Induced by Primordial Scalar Perturbations

Abstract: We derive the complete spectrum of gravitational waves induced by primordial scalar perturbations ranging over all observable wavelengths. This scalar-induced contribution can be computed directly from the observed scalar perturbations and general relativity and is, in this sense, independent of the cosmological model for generating the perturbations. The spectrum is scale invariant on small scales, but has an interesting scale dependence on large and intermediate scales, where scalar-induced gravitational waves do not redshift and are hence enhanced relative to the background density of the Universe. This contribution to the tensor spectrum is significantly different in form from the direct model-dependent primordial tensor spectrum and, although small in magnitude, it dominates the primordial signal for some cosmological models. We confirm our analytical results by direct numerical integration of the equations of motion.

Relativistic fluid dynamics: physics for many different scales

Abstract: The relativistic fluid is a highly successful model used to describe the dynamics of many-particle, relativistic systems. It takes as input basic physics from microscopic scales and yields as output predictions of bulk, macroscopic motion. By inverting the process, an understanding of bulk features can lead to insight into physics on the microscopic scale. Relativistic fluids have been used to model systems as “small” as heavy ions in collisions, and as large as the Universe itself, with “intermediate” sized objects like neutron stars being considered along the way. The purpose of this review is to discuss the mathematical and theoretical physics underpinnings of the relativistic (multiple) fluid model. We focus on the variational principle approach championed by Brandon Carter and his collaborators, in which a crucial element is to distinguish the momenta that are conjugate to the particle number density currents. This approach differs from the “standard” text-book derivation of the equations of motion from the divergence of the stress-energy tensor in that one explicitly obtains the relativistic Euler equation as an “integrability” condition on the relativistic vorticity. We discuss the conservation laws and the equations of motion in detail, and provide a number of (in our opinion) interesting and relevant applications of the general theory.

Linearized dynamics equations for the balance and steer of a bicycle: a benchmark and review

Abstract: We present canonical linearized equations of motion for the Whipple bicycle model consisting of four rigid laterally symmetric ideally hinged parts: two wheels, a frame and a front assembly. The wheels are also axisymmetric and make ideal knife-edge rolling point contact with the ground level. The mass distribution and geometry are otherwise arbitrary. This conservative non-holonomic system has a seven-dimensional accessible configuration space and three velocity degrees of freedom parametrized by rates of frame lean, steer angle and rear wheel rotation. We construct the terms in the governing equations methodically for easy implementation. The equations are suitable for e.g. the study of bicycle self-stability. We derived these equations by hand in two ways and also checked them against two nonlinear dynamics simulations. In the century-old literature, several sets of equations fully agree with those here and several do not. Two benchmarks provide test cases for checking alternative formulations of the equations of motion or alternative numerical solutions. Further, the results here can also serve as a check for general purpose dynamic programs. For the benchmark bicycles, we accurately calculate the eigenvalues (the roots of the characteristic equation) and the speeds at which bicycle lean and steer are self-stable, confirming the century-old result that this conservative system can have asymptotic stability.

Conservative Split-Explicit Time Integration Methods for the Compressible Nonhydrostatic Equations

Abstract: Historically, time-split schemes for numerically integrating the nonhydrostatic compressible equations of motion have not formally conserved mass and other first-order flux quantities. In this paper, split-explicit integration techniques are developed that numerically conserve these properties by integrating prognostic equations for conserved quantities represented in flux form. These procedures are presented for both terrain-following height and hydrostatic pressure (mass) vertical coordinates, two potentially attractive frameworks for which the equation sets and integration techniques differ significantly. For each set of equations, the linear dispersion equation for acoustic/gravity waves is derived and analyzed to determine which terms must be solved in the small (acoustic) time steps and how these terms are represented in the time integration to achieve stability. Efficient techniques for including numerical filters for acoustic and external modes are also presented. Simulations for several idealized test cases in both the height and mass coordinates are presented to demonstrate that these integration techniques appear robust over a wide range of scales, from subcloud to synoptic.

Electron beams and microwave vacuum electronics

Abstract: PREFACE. Introduction. I.1 Outline of the Book. I.2 List of Symbols. I.3 Electromagnetic Fields and Potentials. I.4 Principle of Least Action. Lagrangian. Generalized Momentum. Lagrangian Equations. I.5 Hamiltonian. Hamiltonian Equations. I.6 Liouville Theorem. I.7 Emittance. Brightness. PART I ELECTRON BEAMS. 1 Motion of Electrons in External Electric and Magnetic Static Fields. 1.1 Introduction. 1.2 Energy of a Charged Particle. 1.3 Potential-Velocity Relation (Static Fields). 1.4 Electrons in a Linear Electric Field e0E kx. 1.5 Motion of Electrons in Homogeneous Static Fields. 1.6 Motion of Electrons in Weakly Inhomogeneous Static Fields. 1.6.1 Small Variations in Electromagnetic Fields Acting on Moving Charged Particles. 1.7 Motion of Electrons in Fields with Axial and Plane Symmetry. Busch's Theorem. 2 Electron Lenses. 2.1 Introduction. 2.2 Maupertuis's Principle. Electron-Optical Refractive Index. Differential Equations of Trajectories. 2.3 Differential Equations of Trajectories in Axially Symmetric Fields. 2.4 Differential Equations of Paraxial Trajectories in Axially Symmetric Fields Without a Space Charge. 2.5 Formation of Images by Paraxial Trajectories. 2.6 Electrostatic Axially Symmetric Lenses. 2.7 Magnetic Axially Symmetric Lenses. 2.8 Aberrations of Axially Symmetric Lenses. 2.9 Comparison of Electrostatic and Magnetic Lenses. Transfer Matrix of Lenses . 2.10 Quadrupole lenses. 3 Electron Beams with Self Fields. 3.1 Introduction. 3.2 Self-Consistent Equations of Steady-State Space-Charge Electron Beams. 3.3 Euler's Form of a Motion Equation. Lagrange and Poincare' Invariants of Laminar Flows. 3.4 Nonvortex Beams. Action Function. Planar Nonrelativistic Diode. Perveance. Child-Langmuir Formula. r- and T-Modes of Electron Beams. 3.5 Solutions of Self-Consistent Equations for Curvilinear Space-Charge Laminar Beams. Meltzer Flow. Planar Magnetron with an Inclined Magnetic Field. Dryden Flow. 4 Electron Guns. 4.1 Introduction. 4.2 Pierce's Synthesis Method for Gun Design. 4.3 Internal Problems of Synthesis. Relativistic Planar Diode. Cylindrical and Spherical Diodes. 4.4 External Problems of Synthesis. Cauchy Problem. 4.5 Synthesis of Electrode Systems for Two-Dimensional Curvilinear Beams with Translation Symmetry (Lomax-Kirstein Method). Magnetron Injection Gun. 4.6 Synthesis of Axially Symmetric Electrode Systems. 4.7 Electron Guns with Compressed Beams. Magnetron Injection Gun. 4.8 Explosive Emission Guns. 5 Transport of Space-Charge Beams. 5.1 Introduction. 5.2 Unrippled Axially Symmetric Nonrelativistic Beams in a Uniform Magnetic field. 5.3 Unrippled Relativistic Beams in a Uniform External Magnetic Field. 5.4 Cylindrical Beams in an Infinite Magnetic Field. 5.5 Centrifugal Electrostatic Focusing. 5.6 Paraxial-Ray Equations of Axially Symmetric Laminar Beams. 5.7 Axially Symmetric Paraxial Beams in a Uniform Magnetic Field with Arbitrary Shielding of a Cathode Magnetic Field. 5.8 Transport of Space-Charge Beams in Spatial Periodic Fields. PART II MICROWAVE VACUUM ELECTRONICS. 6 Quasistationary Microwave Devices. 6.1 Introduction. 6.2 Currents in Electron Gaps. Total Current and the Shockley-Ramo Theorem. 6.3 Admittance of a Planar Electron Gap. Electron Gap as an Oscillator. Monotron. 6.4 Equation of Stationary Oscillations of a Resonance Self-Excited Circuit. 6.5 Effects of a Space-Charge Field. Total Current Method. High-Frequency Diode in the r-Mode. Llewellyn-Peterson Equations. 7 Klystrons. 7.1 Introduction. 7.2 Velocity Modulation of an Electron beam. 7.3 Cinematic (Elementary) Theory of Bunching. 7.4 Interaction of a Bunched Current with a Catcher Field. Output Power of A Two-Cavity Klystron. 7.5 Experimental Characteristics of a Two-Resonator Amplifier and Frequency-Multiplier Klystrons. 7.6 Space-Charge Waves in Velocity-Modulated Beams. 7.7 Multicavity and Multibeam Klystron Amplifiers. 7.8 Relativistic Klystrons. 7.9 Reflex Klystrons. 8 Traveling-Wave Tubes and Backward-Wave Oscillators (O-Type Tubes). 8.1 Introduction. 8.2 Qualitative Mechanism of Bunching and Energy Output in a TWTO. 8.3 Slow-Wave Structures. 8.4 Elements of SWS Theory. 8.5 Linear Theory of a Nonrelativistic TWTO. Dispersion Equation, Gain, Effects of Nonsynchronism, Space Charge, and Loss in a Slow-Wave Structure. 8.6 Nonlinear Effects in a Nonrelativistic TWTO. Enhancement of TWTO Efficiency (Velocity Tapering, Depressed Collectors). 8.7 Basic Characteristics and Applications of Nonrelativistic TWTOs. 8.8 Backward-Wave Oscillators. 8.9 Millimeter Nonrelativistic TWTOs, BWOs, and Orotrons. 8.10 Relativistic TWTOs and BWOs. 9 Crossed-Field Amplifiers and Oscillators (M-Type Tubes). 9.1 Introduction. 9.2 Elementary Theory of a Planar MTWT. 9.3 MTWT Amplification. 9.4 M-type Injected Beam Backward-Wave Oscillators (MWO, M-Carcinotron). 9.5 Magnetrons. 9.6 Relativistic Magnetrons. 9.7 Magnetically Insulated Line Oscillators. 9.8 Crossed-Field Amplifiers. 10 Classical Electron Masers and Free Electron Lasers. 10.1 Introduction. 10.2 Spontaneous Radiation of Classical Electron Oscillators. 10.3 Stimulated Radiation of Excited Classical Electron Oscillators. 10.4 Examples of Electron Cyclotron Masers. 10.5 Resonators of Gyromonotrons (Free and Forced Oscillations). 10.6 Theory of a Gyromonotron. 10.7 Subrelativistic Gyrotrons. 10.8 Elements of Gyrotron Electron Optics. 10.9 Mode Interaction and Mode Selection in Gyrotrons. Output Power Systems. 10.10 Gyroklystrons. 10.11 Gyro-Traveling-Wave Tubes. 10.12 Applications of Gyrotrons. 10.13 Cyclotron Autoresonance Masers. 10.14 Free Electron Lasers. Appendixes. 1. Proof of the 3/2 Law for Nonrelativistic Diodes in the r-Mode. 2. Synthesis of Guns for M-Type TWTS and BWOS. 3. Magnetic Field in Axially Symmetric Systems. 4. Dispersion Characteristics of Interdigital and Comb Structures. 5. Electromagnetic Field in Planar Uniform Slow-Wave Structures. 6. Equations of Free Oscillations of Gyrotron Resonators. 7. Derivation of Eqs. (10.66) and (10.67). 8. Calculation of Fourier Coefficients in Gyrotron Equations. 9. Magnetic Systems of Gyrotrons. References. Index.

CoRdE: Cosserat rod elements for the dynamic simulation of one-dimensional elastic objects

Abstract: Simulating one-dimensional elastic objects such as threads, ropes or hair strands is a difficult problem, especially if material torsion is considered. In this paper, we present CoRdE(french 'rope'), a novel deformation model for the dynamic interactive simulation of elastic rods with torsion. We derive continuous energies for a dynamically deforming rod based on the Cosserat theory of elastic rods. We then discretize the rod and compute energies per element by employing finite element methods. Thus, the global dynamic behavior is independent of the discretization. The dynamic evolution of the rod is obtained by numerical integration of the resulting Lagrange equations of motion. We further show how this system of equations can be decoupled and efficiently solved. Since the centerline of the rod is explicitly represented, the deformation model allows for accurate contact and self-contact handling. Thus, we can reproduce many important looping phenomena. Further, a broad variety of different materials can be simulated at interactive rates. Experiments underline the physical plausibility of our deformation model.

Dynamic flight stability of hovering insects

Abstract: The equations of motion of an insect with flapping wings are derived and then simplified to that of a flying body using the “rigid body” assumption. On the basis of the simplified equations of motion, the longitudinal dynamic flight stability of four insects (hoverfly, cranefly, dronefly and hawkmoth) in hovering flight is studied (the mass of the insects ranging from 11 to 1,648 mg and wingbeat frequency from 26 to 157 Hz). The method of computational fluid dynamics is used to compute the aerodynamic derivatives and the techniques of eigenvalue and eigenvector analysis are used to solve the equations of motion. The validity of the “rigid body” assumption is tested and how differences in size and wing kinematics influence the applicability of the “rigid body” assumption is investigated. The primary findings are: (1) For insects considered in the present study and those with relatively high wingbeat frequency (hoverfly, drone fly and bumblebee), the “rigid body” assumption is reasonable, and for those with relatively low wingbeat frequency (cranefly and howkmoth), the applicability of the “rigid body” assumption is questionable. (2) The same three natural modes of motion as those reported recently for a bumblebee are identified, i.e., one unstable oscillatory mode, one stable fast subsidence mode and one stable slow subsidence mode. (3) Approximate analytical expressions of the eigenvalues, which give physical insight into the genesis of the natural modes of motion, are derived. The expressions identify the speed derivative Mu (pitching moment produced by unit horizontal speed) as the primary source of the unstable oscillatory mode and the stable fast subsidence mode and Zw (vertical force produced by unit vertical speed) as the primary source of the stable slow subsidence mode.

An analytic solution of projectile motion with the quadratic resistance law using the homotopy analysis method

Abstract: We consider the problem of two-dimensional projectile motion in which the resistance acting on an object moving in air is proportional to the square of the velocity of the object (quadratic resistance law). It is well known that the quadratic resistance law is valid in the range of the Reynolds number: 1 × 103 ~ 2 × 105 (for instance, a sphere) for practical situations, such as throwing a ball. It has been considered that the equations of motion of this case are unsolvable for a general projectile angle, although some solutions have been obtained for a small projectile angle using perturbation techniques. To obtain a general analytic solution, we apply Liao's homotopy analysis method to this problem. The homotopy analysis method, which is different from a perturbation technique, can be applied to a problem which does not include small parameters. We apply the homotopy analysis method for not only governing differential equations, but also an algebraic equation of a velocity vector to extend the radius of convergence. Ultimately, we obtain the analytic solution to this problem and investigate the validation of the solution.

Photon wave functions, wave-packet quantization of light, and coherence theory

Abstract: The monochromatic Dirac and polychromatic Titulaer?Glauber quantized field theories (QFTs) of electromagnetism are derived from a photon-energy wave function in much the same way that one derives QFT for electrons, i.e., by quantization of a single-particle wave function. The photon wave function and its equation of motion are established from the Einstein energy?momentum?mass relation, assuming a local energy density. This yields a theory of photon wave mechanics (PWM). The proper Lorentz-invariant single-photon scalar product is found to be non-local in coordinate space, and is shown to correspond to orthogonalization of the Titulaer?Glauber wave-packet modes. The wave functions of PWM and mode functions of QFT are shown to be equivalent, evolving via identical equations of motion, and completely describe photonic states. We generalize PWM to two or more photons, and show how to switch between the PWM and QFT viewpoints. The second-order coherence tensors of classical coherence theory and the two-photon wave functions are shown to propagate equivalently. We give examples of beam-like states, which can be used as photon wave functions in PWM, or modes in QFT. We propose a practical mode converter based on spectral filtering to convert between wave packets and their corresponding biorthogonal dual wave packets.

Fundamentals of Airplane Flight Mechanics

Abstract: Flight mechanics is the application of Newton's laws to the study of vehicle trajectories (performance), stability, and aerodynamic control. This text is concerned with the derivation of analytical solutions of airplane flight mechanics problems associated with flight in a vertical plane. Algorithms are presented for calculating lift, drag, pitching moment, and stability derivatives. Flight mechanics is a discipline. As such, it has equations of motion, acceptable approximations, and solution techniques for the approximate equations of motion. Once an analytical solution has been obtained, numbers are calculated in order to compare the answer with the assumptions used to derive it and to acquaint students with the sizes of the numbers. A subsonic business jet is used for these calculations.

Thermostats for “Slow” Configurational Modes

Abstract: Thermostats are dynamical equations used to model thermodynamic variables such as temperature and pressure in molecular simulations. For computationally intensive problems such as the simulation of biomolecules, we propose to average over fast momentum degrees of freedom and construct thermostat equations in configuration space. The equations of motion are deterministic analogues of the Smoluchowski dynamics in the method of stochastic differential equations.

On the dynamics of rocking motion of single rigid–block structures

Abstract: This paper describes the behavior of single rigid-block structures under dynamic loading. A comprehensive experimental investigation has been carried out to study the rocking response of four blue granite stones with different geometrical characteristics under free vibration, and harmonic and random motions of the base. In total, 275 tests on a shaking table were carried out in order to address the issues of repeatability of the results and stability of the rocking motion response. Two different tools for the numerical simulations of the rocking motion of rigid blocks are considered. The first tool is analytical and overcomes the usual limitations of the traditional piecewise equations of motion through a Lagrangian formalism. The second tool is based on the discrete element method (DEM), especially effective for the numerical modeling of rigid blocks. A new methodology is proposed for finding the parameters of the DEM by using the parameters of the classical theory. An extensive comparison between numerical and experimental data has been carried out to validate and define the limitations of the analytical tools under study. Copyright © 2007 John Wiley & Sons, Ltd.

Dynamics of quantum dissipation systems interacting with bosonic canonical bath: hierarchical equations of motion approach.

Abstract: A nonperturbative theory is developed, aiming at an exact and efficient evaluation of a general quantum system interacting with arbitrary bath environment at any temperature and in the presence of arbitrary time-dependent external fields. An exact hierarchical equations of motion formalism is constructed on the basis of a calculus-on-path-integral algorithm, via the auxiliary influence generating functionals related to the interaction bath correlation functions in a parametrization expansion form. The corresponding continued-fraction Green's functions formalism for quantum dissipation is also presented. Proposed further is the principle of residue correction, not just for truncating the infinite hierarchy, but also for incorporating the small residue dissipation that may arise from the practical difference between the true and parametrized bath correlation functions. The final residue-corrected hierarchical equations of motion can therefore be used practically for the evaluation of arbitrary dissipative quantum systems.

The mathematical analysis of electrical and optical wave-motion on the basis of Maxwell's equations

Abstract: Rarebooksclub.com, United States, 2012. Paperback. Book Condition: New. 246 x 189 mm. Language: English . Brand New Book ***** Print on Demand *****.This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1915 Excerpt: .the integral expressions forll, nxi n2in these equations and equating to zero the coefficients of functions of type Jn(Xp) in the resulting integral equation, we obtain the system of equations IV THE SPREADING OF WAVES OVER AN INFINITE PLANE 75 where the last equation has been simplified with the aid of the relations / = g = 0 (n0) which are a consequence of the previous equations. Solving these equations we eventually find that if iWQ o, Qt), n, (j?., o, n, ), + IB cos oS Jx (p) eTMla---5-r. Jo (I + m) (hH + km) The directed effect depends on the presence of the terms involving cos oS in the expressions for Qz and Rz. Now when r = oo for the second medium, h = cc, and these terms vanish altogether; hence the possibility of directing the energy of the radiation sent out...

Free vibration analysis of functionally graded cylindrical shells including thermal effects

Abstract: Free vibration analysis of simply supported FG cylindrical shells for four sets of in-plane boundary conditions is performed. The material properties are assumed to be temperature-dependant and gradually changed in the thickness direction of the shell. The effects of temperature rise are investigated by specifying arbitrary high temperature on the outer surface and the ambient temperature on the inner surface of the cylinder. Distribution of temperature across the shell thickness is found from steady state heat conduction only in the thickness direction. The equations of motion are based on Love's shell theory and the von Karman–Donnell-type of kinematic nonlinearity. The static analysis is first performed to determine the prestressed state induced by the thermal loadings, using the exact solution of the governing equations and then the equations of motion are solved by Galerkin's method. The results are obtained to indicate the effects of power law index on the natural frequencies and corresponding mode shapes in the thermal environment.

Unified view on multiconfigurational time propagation for systems consisting of identical particles.

Abstract: We show that the successful and formally exact multiconfigurational time-dependent Hartree method (MCTDH) takes on a unified and compact form when specified for systems of identical particles (MCTDHF for fermions MCTDHB for bosons). In particular the equations of motion for the orbitals depend explicitly and solely on the reduced one- and two-body density matrices of the system’s many-particle wave function. We point out that this appealing representation of the equations of motion opens up further possibilities for approximate propagation schemes.

Continuous Limit of Discrete Systems with Long-Range Interaction

Abstract: Discrete systems with long-range interactions are considered. Continuous medium models as continuous limit of discrete chain system are defined. Long-range interactions of chain elements that give the fractional equations for the medium model are discussed. The chain equations of motion with long-range interaction are mapped into the continuum equation with the Riesz fractional derivative. We formulate the consistent definition of continuous limit for the systems with long-range interactions. In this paper, we consider a wide class of long-range interactions that give fractional medium equations in the continuous limit. The power-law interaction is a special case of this class.

Lie group variational integrators for the full body problem in orbital mechanics

Abstract: Equations of motion, referred to as full body models, are developed to describe the dynamics of rigid bodies acting under their mutual gravitational potential. Continuous equations of motion and discrete equations of motion are derived using Hamilton’s principle. These equations are expressed in an inertial frame and in relative coordinates. The discrete equations of motion, referred to as a Lie group variational integrator, provide a geometrically exact and numerically efficient computational method for simulating full body dynamics in orbital mechanics; they are symplectic and momentum preserving, and they exhibit good energy behavior for exponentially long time periods. They are also efficient in only requiring a single evaluation of the gravity forces and moments per time step. The Lie group variational integrator also preserves the group structure without the use of local charts, reprojection, or constraints. Computational results are given for the dynamics of two rigid dumbbell bodies acting under their mutual gravity; these computational results demonstrate the superiority of the Lie group variational integrator compared with integrators that are not symplectic or do not preserve the Lie group structure.

Perspective on classical strings from complex sine-Gordon solitons

Abstract: We study a family of classical string solutions with large spins on R{sub t}xS{sup 3} subspace of AdS{sub 5}xS{sup 5} background, which are related to Complex sine-Gordon solitons via Pohlmeyer's reduction. The equations of motion for the classical strings are cast into Lame equations and Complex sine-Gordon equations. We solve them under periodic boundary conditions, and obtain analytic profiles for the closed strings. They interpolate two kinds of known rigid configurations with two spins: on one hand, they reduce to folded or circular spinning/rotating strings in the limit where a soliton velocity goes to zero, while on the other hand, the dyonic giant magnons are reproduced in the limit where the period of a kink-array goes to infinity.

On the well-posedness for the Euler-Korteweg model in several space dimensions

Abstract: The Euler-Korreweg model results from a modification of the standard Euler equations governing the motion of compressible inviscid fluids through the adjunction of the Korteweg stress tensor, which takes into account capillarity effects in regions where the density experiences large variations, typically across interfaces for fluids exhibiting phase changes. One of the main difficulties in the analysis of the Cauchy problem for this model, a third order system of conservation laws, is the absence of dissipative regularization, since viscosity is neglected. The Cauchy problem for isothermal fluids in one space dimension has been addressed by the authors in an earlier paper, using Lagrangian coordinates. Here the Cauchy problem is investigated in arbitrary space dimension N, still for isothermal fluids, and a variable capillarity coefficient. A local well-posedness result is obtained in Sobolev spaces as though the density gradient and the velocity field were solutions of a symmetrizable hyperbolic system. More precisely, well-posedness is shown for Hs+1 x H-s (s > N/2 + 1) perturbations of smooth global solutions, either constant states or traveling profiles. In addition, almost-global existence is proved for small enough perturbations, and a blow-up criterion is shown. Proofs rely on a suitable extended formulation of the system, which turns out to amount to a nonlinear degenerate Schrodinger equation coupled with a transport equation, and on a priori estimates without loss of derivatives for the extended system, which necessitate various 'gauge' functions to cancel out bad commutators.