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" Dynamic stability of bodies containing fluid. "
N N Moiseev
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BL
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754789
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b574751
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N N Moiseev
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Dynamic stability of bodies containing fluid.\ N N Moiseev
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| Publication Statement
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[Place of publication not identified] : Springer, 2012
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| ISBN
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364286452X
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: 9783642864520
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| Contents
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One. Dynamics and Stability of Rigid Bodies Containing a Fluid.- 1. Equations of Motion of a Rigid Body with Fluid Containing Cavities.- 1-1. The Hamilton-Ostrogradskiy Principle.- 1-2. Some Formulas of Kinematics and Vector Analysis.- 1-3. Basic Dynamic Parameters.- 1-4. Derivation of the Equations of Motion of an Unconstrained Rigid Body Containing a Fluid.- 1-5. Lagrange's Equations.- 1-6. Forces Exerted by the Fluid on the Rigid Body.- 1-7. Equations of Motion of the System Relative to the Mass Center.- 1-8. Integrals of the Equations of Motion.- 1-9. Viscous Fluids.- 2. Elementary Cases of Motion of a Rigid Body Containing a Fluid.- 2-1. Irrotational Motion of a Fluid.- 2-2. Motion of a Fluid-Containing Rigid Body. Zhukov skiy's Theorem.- 2-3. Velocity Potentials and Moments of Inertia of Equivalent Bodies for Several Cavity Shapes.- 2-4. Homogeneous Vortex Flow of a Fluid.- 2-5. Problems of Stability of Motion. Lyapunov's and Chetayev's Theorems.- 2-6. Steady Screw Displacement of a Body Containing a Fluid.- 2-7. Uniform Rotation of a Body About a Stationary Point.- 2-8. Permanent Rotation of a Hydrostat Moving by Inertia About a Stationary Point.- 2-9. Stability of Rotation of a Rigid Body with an Ellipsoidal Cavity.- 3. Stability of Motion with Respect to a Part of the Variables of a Rigid Body with Cavities Partially Filled with a Fluid.- 3-1. Statement of the Problem.- 3-2. Application of the Method of Lyapunov's Functions to Problems of Stability with Respect to a Part of the Variables.- 3-3. Stability of Motion of a Rotating Body Filled with a Viscous Fluid.- 3-4. Stability of Constant Inertial Screw Motion of a Body Containing a Fluid.- 3-5. Stability of Circular Motion of an Artificial Satellite Containing a Fluid.- 3-6. Stability of Rotational Motions of a Fluid-Filled Projectile.- 3-7. Stability of the Equilibrium of a Fluid-Containing Pendulum.- 4. Stability of Steady Motion of Rigid Bodies with Fluid-Filled Cavities.- 4-1. Equations of Equilibrium and of Steady Motions.- 4-2. Statement of the Problem of Stability of Steady Motion.- 4-3. Some Theorems Concerning the Stability of Steady Motions.- 4-4. The Problem of the Minimum.- 4-5. Stability of Motion of an Artificial Satellite Moving in a Circular Orbit.- 4-6. Stability of Rotation of a Rigid Body Containing a Fluid About a Fixed Axis.- 4-7. Stability of the Relative Equilibrium of a Physical Pendulum Containing a Fluid.- Two. Vibrations of a Fluid and of the Body Containing the Fluid.- 5. Statement of the Problems of the Theory of Vibrations.- 5-1. Vibrations of a Massive Fluid Contained in a Vessel.- 5-2. Vibration of a Fluid in a Field of Variable-Intensity Mass Forces.- 5-3. The Ritz Method in the Stokes-Zhukovskiy Problem.- 5-4. The Pendulum Problem.- 5-5. Vibration of a Conservative System with Fluid Links.- 5-6. Problem of Torsional Oscillations of a Beam with a Fluid-Containing Cavity.- 5-7. Equations of Torsional-Flexural Oscillations of a Fluid- Containing Beam.- 6. General Properties of Equations of Vibrations of Bodies Containing a Fluid.- 6-1. Vibrations of a Fluid Confined in a Vessel.- 6-2. Equations of Vibrations of a Conservative System with a Fluid Link.- 6-3. General Equations for the Oscillations of a Beam with a Fluid-Containing Cavity.- 6-4. Study of the Positive Definiteness of Operator M.- 6-5. Some Problems of the Theory of Forces Suddenly Applied to a Body Containing a Fluid.- 6-6. Concerning the Oscillations of Bodies Floating in a Reservoir of Limited Dimensions.- 7. Fluid Surface Phenomena and Their Effect on the Motion of a Body Containing a Fluid.- 7-1. Statement of Problems of the Theory of Vibrations.- 7-2. Problem of the Equilibrium Configuration of the Free Surface.- 7-3. The Theory of Small Vibrations.- 1-A. Problems of Dynamics of a Bubble.- 1-5. Asymptotic Behavior for "Shallow Water".- Appendix. Formulating the Problem of the Motion of a Fluid Subjected to Gravity Forces and Surface Tension Forces.- 8. Vibrations of a Viscous Fluid and of a Body Containing a Viscous Fluid.- 8-1. Elementary Problems of the Vibrations of a Viscous Fluid with a Large.- Reynolds Number.- 8-2. Vibration of an Open Vessel Containing a Viscous Fluid.- 8-3. Three-Dimensional Problems of the Theory of Vibrations of Viscous Fluid.- Editor's Supplement to the References.- References.
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N N Moiseev
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