Principles of Dynamics

I . Gravitational Theory of Planetary Systems

1.1 Introductory Remarks

1.2 Frame of Reference and Unit of Length

1.3 Time Scale and Units

1.4 Keplerian Laws of Planetary Motion

1.5 Newtonian Postulate

1.6 Newtonian Frame: First Law of Motion

1.7 Motion of Two Gravitating Bodies

1.8 Three Gravitating Bodies: Lagrange Configurations

1.9 The Restricted Problem of 3 Bodies

1.10 The n-Body Problem: First Integrals

1.11 Dispersion of an n-Body System

1.12 Some Inequalities for an w-Body System

1.13 Generalized Newtonian Postulate

1.14 Gravitational Potential and Potential Energy

1.15 Some Properties of Gravitational Fields

1.16 Mutual Fields of Distant Bodies

1.17 Fields of Axisymmetric Bodies

1.18 Gravity and the Figure of the Earth

Exercises

II. Foundations of Mechanics: General Principles

2.1 Frames of Reference and Rates of Change

2.2 Motion Relative to the Earth

2.3 Motion under Independent Constraint

2.4 Foucault Pendulum Experiment

2.5 Axisymmetric Constraint: Stability and Range of Motion

2.6 Inertial Mass

2.7 Force: Second and Third Laws of Motion

2.8 Fictitious Body-forces

2.9 Continuum Dynamics: Preliminary Notions

2.10 Continuum Dynamics: Equations of Motion

2.11 Stress Analysis in a Continuum

2.12 Principles of Work and Energy

Exercises

III. General Motion of a Rigid Body

3.1 Kinematics

3.2 Dynamical Basis

3.3 Application of the Principles

3.4 Properties of the Inertia Tensor

3.5 Impulse and Inertia

3.6 Differential Equations of Euler

3.7 Free Rotation of a General Body

3.8 Steady States: Precession

3.9 Gyrodynamics

Exercises

Index