(Ebook) Advanced dynamics 1st Edition by Donald T Greenwood ISBN 9780521029933 0521029937

1 Introduction to particle dynamics

1.1 Particle motion

The laws of motion for a particle

Kinematics of particle motion

Velocity and acceleration expressions for common coordinate systems

Cylindrical coordinates

Spherical coordinates

Tangential and normal components

Relative motion and rotating frames

Instantaneous center of rotation

1.2 Systems of particles

Equations of motion

Angular momentum

Accelerating frames

Work and energy

Conservation of energy

Friction

Linear damping

Coulomb friction

1.3 Constraints and configuration space

Generalized coordinates and configuration space

Holonomic constraints

Nonholonomic constraints

Other constraint classifications

Accessibility

Exactness and integrability

1.4 Work, energy and momentum

Virtual displacements

Virtual work

Principle of virtual work

Kinetic energy

Potential energy

Generalized momentum

1.5 Impulse response

Linear impulse and momentum

Angular impulse and momentum

Collisions

Generalized impulse and momentum

Impulse and energy

1.6 Bibliography

1.7 Problems

2 Lagrange’s and Hamilton’s equations

2.1 D’Alembert’s principle and Lagrange’s equations

D’Alembert’s principle

Lagrange’s equations

2.2 Hamilton’s equations

Canonical equations

Form of the Hamiltonian function

Other Hamiltonian equations

2.3 Integrals of the motion

Conservative system

Ignorable coordinates

2.4 Dissipative and gyroscopic forces

Rayleigh’s dissipation function

Gyroscopic forces

Coulomb friction

2.5 Configuration space and phase space

Configuration space

Phase space

Velocity space

2.6 Impulse response, analytical methods

Hamiltonian approach

Lagrangian approach

Constrained impulsive motion

Lagrange multiplier form

Impulsive constraints

Energy relations

Impulsive constraints

2.7 Bibliography

2.8 Problems

3 Kinematics and dynamics of a rigid body

3.1 Kinematical preliminaries

Degrees of freedom

Rotation of axes

Euler angles

Axis and angle of rotation

Euler parameters

Successive rotations

Angular velocity

Inflnitesimal rotations

Instantaneous axis of rotation

3.2 Dyadic notation

Definition of a dyadic

Dyadic operations

3.3 Basic rigid body dynamics

Kinetic energy

Vectorial dynamics, Euler equations

Ellipsoid of inertia

Modified Euler equations

Lagrange’s equations

Angular velocity coefficients

Free rotational motion

Axial symmetry

The Poinsot method

Axial symmetry

3.4 Impulsive motion

Planar rigid body motion

Constrained impulse response

Quasi-velocities

Input–output methods

3.5 Bibliography

3.6 Problems

4 Equations of motion: differential approach

4.1 Quasi-coordinates and quasi-velocities

Transformation equations

Constraints

4.2 Maggi’s equation

Derivation of Maggi’s equation

4.3 The Boltzmann–Hamel equation

Derivation

4.4 The general dynamical equation

D’Alembert’s principle

Rigid body equations

4.5 A fundamental equation

System of particles

System of rigid bodies

Volterra’s equation

4.6 The Gibbs–Appell equation

System of particles

System of rigid bodies

Principle of least constraint

4.7 Constraints and energy rates

Ideal and conservative constraints

Conservative system

Work and energy rates

4.8 Summary of differential methods

A note no quasi-velocities

4.9 Bibliography

4.10 Problems

5 Equations of motion: integral approach

5.1 Hamilton’s principle

Holonomic system

Nonholonomic system

5.2 Transpositional relations

The d and Delta operators

Nonholonomic constraints

The theorem of Frobenius

Geometrical considerations

5.3 The Boltzmann–Hamel equation, transpositional form

Derivation

5.4 The central equation

Derivation

Explicit form

5.5 Suslov’s principle

Dependent and independent coordinates

Suslov’s principle

Equations of motion

5.6 Summary of integral methods

5.7 Bibliography

5.8 Problems

6 Introduction to numerical methods

6.1 Interpolation

Polynomial approximations

Lagrange’s interpolation formula

Divided difference

Forward and backward differences

6.2 Numerical integration

Euler’s method

Truncation errors

Roundoff errors

Trapezoidal method

Modified Euler method

Runge–Kutta methods

Adams–Bashforth predictors

Adams–Moulton correctors

Truncation errors of predictor–corrector methods

Special integration algorithms

6.3 Numerical stability

Euler integration

Trapezoidal method

Runge–Kutta methods

Midpoint method

Extraneous roots

6.4 Frequency response methods

Transfer functions

Free sinusoidal response

Case 1

Case 2

Case 3

Case 4

Numerical comparisons

6.5 Kinematic constraints

Baumgarte’s method for holonomic constraints

Baumgarte’s method for nonholonomic constraints

One-step method for holonomic constraints

One-step method for nonholonomic constraints

A comparison of constraint enforcement methods

Euler parameter constraints

6.6 Energy and momentum methods

Energy corrections

Work and energy

First method

Second method

Conservation of momentum

Angular momentum corrections

6.7 Bibliography

6.8 Problems

Appendix

A.1 Answers to problems

Chapter 1

Chapter 2

Chapter 3

Chapter 4

Chapter 5

Chapter 6

Index