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Methods of Analytical Dynamics

ISBN-10: 0486432394
ISBN-13: 9780486432397
Edition: 2003
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Description: A balanced presentation that encompasses both formalism and structure in analytical dynamics, this graduate-level text discusses fundamentals of Newtonian and analytical mechanics, motion relative to rotating reference frames, rigid body dynamics,  More...

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Book details

List price: $32.95
Copyright year: 2003
Publisher: Dover Publications, Incorporated
Publication date: 5/20/2010
Binding: Paperback
Pages: 544
Size: 5.50" wide x 8.75" long x 1.25" tall
Weight: 1.474

A balanced presentation that encompasses both formalism and structure in analytical dynamics, this graduate-level text discusses fundamentals of Newtonian and analytical mechanics, motion relative to rotating reference frames, rigid body dynamics, behavior of dynamical systems, geometric theory, stability of multi-degree-of-freedom autonomous and nonautonomous systems, and analytical solutions by perturbation techniques. Later chapters cover transformation theory, the Hamilton-Jacobi equation, theory and applications of the gyroscope, and problems in celestial mechanics and spacecraft dynamics. Two helpful appendixes offer additional information on dyadics and topology and modern analysis. 1970 edition. 128 figures.

Fundamentals of Newtonian Mechanics
Historical Survey of Mechanics
Newton's Laws
Impulse and Momentum
Moment of a Force and Angular Momentum
Work and Energy
Energy Diagrams
Systems of Particles
The Two-Body Central Force Problem
The Inverse Square Law. Orbits of Planets and Satellites
Scattering by a Repulsive Central Force
Suggested References
Fundamentals of Analytical Mechanics
Degrees of Freedom. Generalized Coordinates
Systems with Constraints
The Stationary Value of a Function
The Stationary Value of a Definite Integral
The Principle of Virtual Work
D'Alembert's Principle
Hamilton's Principle
Lagrange's Equations of Motion
Lagrange's Equations for Impulsive Forces
Conservation Laws
Routh's Method for the Ignoration of Coordinates
Rayleigh's Dissipation Function
Hamilton's Equations
Suggested References
Motion Relative to Rotating Reference Frames
Transformation of Coordinates
Rotating Coordinate Systems
Expressions for the Motion in Terms of Moving Reference Frames
Motion Relative to the Rotating Earth
Motion of a Free Particle Relative to the Rotating Earth
Foucault's Pendulum
Suggested References
Rigid Body Dynamics
Kinematics of a Rigid Body
The Linear and Angular Momentum of a Rigid Body
Translation Theorem for the Angular Momentum
The Kinetic Energy of a Rigid Body
Principal Axes
The Equations of Motion for a Rigid Body
Euler's Equations of Motion
Euler's Angles
Moment-Free Inertially Symmetric Body
General Case of a Moment-Free Body
Motion of a Symmetric Top
The Lagrangian Equations for Quasi-Coordinates
The Equations of Motion Referred to an Arbitrary System of Axes
The Rolling of a Coin
Suggested References
Behavior of Dynamical Systems. Geometric Theory
Fundamental Concepts
Motion of Single-Degree-of-Freedom Autonomous Systems about Equilibrium Points
Conservative Systems. Motion in the Large
The Index of Poincare
Limit Cycles of Poincare
Suggested References
Stability of Multi-Degree-of-Freedom Autonomous Systems
General Linear Systems
Linear Autonomous Systems
Stability of Linear Autonomous Systems. Routh-Hurwitz Criterion
The Variational Equations
Theorem on the First-Approximation Stability
Variation from Canonical Systems. Constant Coefficients
The Liapunov Direct Method
Geometric Interpretation of the Liapunov Direct Method
Stability of Canonical Systems
Stability in the Presence of Gyroscopic and Dissipative Forces
Construction of Liapunov Functions for Linear Autonomous Systems
Suggested References
Nonautonomous Systems
Linear Systems with Periodic Coefficients. Floquet's Theory
Stability of Variational Equations with Periodic Coefficients
Orbital Stability
Variation from Canonical Systems. Periodic Coefficients
Second-Order Systems with Periodic Coefficients
Hill's Infinite Determinant
Mathieu's Equation
The Liapunov Direct Method
Suggested References
Analytical Solutions by Perturbation Techniques
The Fundamental Perturbation Technique
Secular Terms
Lindstedt's Method
The Krylov-Bogoliubov-Mitropolsky (KBM) Method
A Perturbation Technique Based on Hill's Determinants
Periodic Solutions of Nonautonomous Systems. Duffing's Equation
The Method of Averaging
Suggested References
Transformation Theory. The Hamilton-Jacobi Equation
The Principle of Least Action
Contact Transformations
Further Extensions of the Concept of Contact Transformations
Integral Invariants
The Lagrange and Poisson Brackets
Infinitesimal Contact Transformations
The Hamilton-Jacobi Equation
Separable Systems
Action and Angle Variables
Perturbation Theory
Suggested References
The Gyroscope: Theory and Applications
Oscillations of a Symmetric Gyroscope
Effect of Gimbal Inertia on the Motion of a Free Gyroscope
Effect of Rotor Shaft Flexibility on the Frequency of Oscillation of a Free Gyroscope
The Gyrocompass
The Gyropendulum. Schuler Tuning
Rate and Integrating Gyroscopes
Suggested References
Problems in Celestial Mechanics
Kepler's Equation. Orbit Determination
The Many-Body Problem
The Three-Body Problem
The Restricted Three-Body Problem
Stability of Motion Near the Lagrangian Points
The Equations of Relative Motion. Disturbing Function
Gravitational Potential and Torques for an Arbitrary Body
Precession and Nutation of the Earth's Polar Axis
Variation of the Orbital Elements
The Resolution of the Disturbing Function
Suggested References
Problems in Spacecraft Dynamics
Transfer Orbits. Changes in the Orbital Elements Due to a Small Impulse
Perturbations of a Satellite Orbit in the Gravitational Field of an Oblate Planet
The Effect of Atmospheric Drag on Satellite Orbits
The Attitude Motion of Orbiting Satellites. General Considerations
The Attitude Stability of Earth-Pointing Satellites
The Attitude Stability of Spinning Symmetrical Satellites
Variable-Mass Systems
Rocket Dynamics
Suggested References
Elements of Topology and Modern Analysis
Sets and Functions
Metric Spaces
Topological Spaces
Suggested References
Name Index
Subject Index

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