Methods of analytical dynamics

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Methods of analytical dynamics / Leonard Meirovitch

資料種別:: 図書
出版情報:: Mineola, N.Y. : Dover, 2003
形態:: xv, 524 p. ; 22 cm
著者名:: Meirovitch, Leonard <DA00050268>
ISBN:: 9780486432397 [0486432394] (pbk.)
書誌ID:: BA69204373

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注記:

Originally published: New York : McGraw-Hill, 1970, in series: Advanced engineering series
Includes bibliographical references and indexes

主題:

Dynamics

言語:

英語

目次情報:

Preface

Fundamentals of Newtonian Mechanics / Chapter 1：

Historical Survey of Mechanics / 1.1：

Newton's Laws / 1.2：

Impulse and Momentum / 1.3：

Moment of a Force and Angular Momentum / 1.4：

Work and Energy / 1.5：

Energy Diagrams / 1.6：

Systems of Particles / 1.7：

The Two-Body Central Force Problem / 1.8：

The Inverse Square Law. Orbits of Planets and Satellites / 1.9：

Scattering by a Repulsive Central Force / 1.10：

Problems

Suggested References

Fundamentals of Analytical Mechanics / Chapter 2：

Degrees of Freedom. Generalized Coordinates / 2.1：

Systems with Constraints / 2.2：

The Stationary Value of a Function / 2.3：

The Stationary Value of a Definite Integral / 2.4：

The Principle of Virtual Work / 2.5：

D'Alembert's Principle / 2.6：

Hamilton's Principle / 2.7：

Lagrange's Equations of Motion / 2.8：

Lagrange's Equations for Impulsive Forces / 2.9：

Conservation Laws / 2.10：

Routh's Method for the Ignoration of Coordinates / 2.11：

Rayleigh's Dissipation Function / 2.12：

Hamilton's Equations / 2.13：

Motion Relative to Rotating Reference Frames / Chapter 3：

Transformation of Coordinates / 3.1：

Rotating Coordinate Systems / 3.2：

Expressions for the Motion in Terms of Moving Reference Frames / 3.3：

Motion Relative to the Rotating Earth / 3.4：

Motion of a Free Particle Relative to the Rotating Earth / 3.5：

Foucault's Pendulum / 3.6：

Rigid Body Dynamics / Chapter 4：

Kinematics of a Rigid Body / 4.1：

The Linear and Angular Momentum of a Rigid Body / 4.2：

Translation Theorem for the Angular Momentum / 4.3：

The Kinetic Energy of a Rigid Body / 4.4：

Principal Axes / 4.5：

The Equations of Motion for a Rigid Body / 4.6：

Euler's Equations of Motion / 4.7：

Euler's Angles / 4.8：

Moment-Free Inertially Symmetric Body / 4.9：

General Case of a Moment-Free Body / 4.10：

Motion of a Symmetric Top / 4.11：

The Lagrangian Equations for Quasi-Coordinates / 4.12：

The Equations of Motion Referred to an Arbitrary System of Axes / 4.13：

The Rolling of a Coin / 4.14：

Behavior of Dynamical Systems. Geometric Theory / Chapter 5：

Fundamental Concepts / 5.1：

Motion of Single-Degree-of-Freedom Autonomous Systems about Equilibrium Points / 5.2：

Conservative Systems. Motion in the Large / 5.3：

The Index of Poincare / 5.4：

Limit Cycles of Poincare / 5.5：

Stability of Multi-Degree-of-Freedom Autonomous Systems / Chapter 6：

General Linear Systems / 6.1：

Linear Autonomous Systems / 6.2：

Stability of Linear Autonomous Systems. Routh-Hurwitz Criterion / 6.3：

The Variational Equations / 6.4：

Theorem on the First-Approximation Stability / 6.5：

Variation from Canonical Systems. Constant Coefficients / 6.6：

The Liapunov Direct Method / 6.7：

Geometric Interpretation of the Liapunov Direct Method / 6.8：

Stability of Canonical Systems / 6.9：

Stability in the Presence of Gyroscopic and Dissipative Forces / 6.10：

Construction of Liapunov Functions for Linear Autonomous Systems / 6.11：

Nonautonomous Systems / Chapter 7：

Linear Systems with Periodic Coefficients. Floquet's Theory / 7.1：

Stability of Variational Equations with Periodic Coefficients / 7.2：

Orbital Stability / 7.3：

Variation from Canonical Systems. Periodic Coefficients / 7.4：

Second-Order Systems with Periodic Coefficients / 7.5：

Hill's Infinite Determinant / 7.6：

Mathieu's Equation / 7.7：

Analytical Solutions by Perturbation Techniques / 7.8：

The Fundamental Perturbation Technique / 8.1：

Secular Terms / 8.2：

Lindstedt's Method / 8.3：

The Krylov-Bogoliubov-Mitropolsky (KBM) Method / 8.4：

A Perturbation Technique Based on Hill's Determinants / 8.5：

Periodic Solutions of Nonautonomous Systems. Duffing's Equation / 8.6：

The Method of Averaging / 8.7：

Transformation Theory. The Hamilton-Jacobi Equation / Chapter 9：

The Principle of Least Action / 9.1：

Contact Transformations / 9.2：

Further Extensions of the Concept of Contact Transformations / 9.3：

Integral Invariants / 9.4：

The Lagrange and Poisson Brackets / 9.5：

Infinitesimal Contact Transformations / 9.6：

The Hamilton-Jacobi Equation / 9.7：

Separable Systems / 9.8：

Action and Angle Variables / 9.9：

Perturbation Theory / 9.10：

The Gyroscope: Theory and Applications / Chapter 10：

Oscillations of a Symmetric Gyroscope / 10.1：

Effect of Gimbal Inertia on the Motion of a Free Gyroscope / 10.2：

Effect of Rotor Shaft Flexibility on the Frequency of Oscillation of a Free Gyroscope / 10.3：

The Gyrocompass / 10.4：

The Gyropendulum. Schuler Tuning / 10.5：

Rate and Integrating Gyroscopes / 10.6：

Problems in Celestial Mechanics / Chapter 11：

Kepler's Equation. Orbit Determination / 11.1：

The Many-Body Problem / 11.2：

The Three-Body Problem / 11.3：

The Restricted Three-Body Problem / 11.4：

Stability of Motion Near the Lagrangian Points / 11.5：

The Equations of Relative Motion. Disturbing Function / 11.6：

Gravitational Potential and Torques for an Arbitrary Body / 11.7：

Precession and Nutation of the Earth's Polar Axis / 11.8：

Variation of the Orbital Elements / 11.9：

The Resolution of the Disturbing Function / 11.10：

Problems in Spacecraft Dynamics / Chapter 12：

Transfer Orbits. Changes in the Orbital Elements Due to a Small Impulse / 12.1：

Perturbations of a Satellite Orbit in the Gravitational Field of an Oblate Planet / 12.2：

The Effect of Atmospheric Drag on Satellite Orbits / 12.3：

The Attitude Motion of Orbiting Satellites. General Considerations / 12.4：

The Attitude Stability of Earth-Pointing Satellites / 12.5：

The Attitude Stability of Spinning Symmetrical Satellites / 12.6：

Variable-Mass Systems / 12.7：

Rocket Dynamics / 12.8：

Dyadics / Appendix A：

Elements of Topology and Modern Analysis / Appendix B：

Sets and Functions / B.1：

Metric Spaces / B.2：

Topological Spaces / B.3：

Name Index

Subject Index

Preface

Fundamentals of Newtonian Mechanics / Chapter 1：

Historical Survey of Mechanics / 1.1：

Newton's Laws / 1.2：

Impulse and Momentum / 1.3：

Moment of a Force and Angular Momentum / 1.4：

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