Dynamics

Chapter I. Introduction to the Calculus of Vectors 1.1 Fundamental ideas 1.2 Vectors 1.3 Summary of Vector algebra 1.4 Velocity and acceleration 1.5 Integration of vector functions 1.6 Vector fields 1.7 Elements of particle kinematics 1.8 Rectangular Cartesian coordinates 1.9 Normal and tangential coordinates 1.10 Plane and cylindrical polar coordinates 1.11 Spherical polar coordinates Chapter II. Theory of Particle motion 2.1 Introduction 2.2 Newton's Laws of motion; mass and force 2.3 Units 2.4 Impulse and momentum 2.5 Impulsive forces 2.6 Power, work, and kinetic energy 2.7 Force fields and potential energy 2.8 Mechanical energy and conservation of energy Chapter III. Applications in particle motion 3.1 Introduction 3.2 The uniform force field 3.3 Simple harmonic motion 3.4 Effect of a periodic disturbing force 3.5 Central force motion 3.6 Central repulsive force 3.7 Dissipative forces Chapter IV. Dynamics of particle systems and plane rigid bodies 4.1 Introduction 4.2 Relative motion of two particles 4.3 Dynamics of multiparticle systems 4.4 Kinematics of plane rigid bodies 4.5 Dynamics of plane systems 4.6 Impulse-momentum principles for systems 4.7 The work-energy principle for particle systems and plane rigid bodies 4.8 Work and energy for general plane systems; real and ideal constraints Chapter V. Technical application in plane motion 5.1 Introduction 5.2 Elementary analysis; force and acceleration at particular instants 5.3 Impact and impulsive motion 5.4 Variable mass 5.5 Conservative systems Chapter VI. Rigid-body dynamics in Three dimensions 6.1 Introduction to rigid-body kinematics in space 6.2 General displacement of a rigid body; finite rotations and Euler's theorem 6.3 Small rotations of a rigid body; angular velocity 6.4 Rotating coordinates; general relative motion equations 6.5 The angular momentum of a rigid body; moments and products of inertia 6.6 The kinetic energy of a rigid body; the work-energy principle 6.7 Special forms of the dynamical equations; Euler's equations 6.8 Equilibrium of a rigid body Chapter VII. Three-dimensional applications of the principles of dynamics 7.1 Introduction 7.2 Effects of the Earth's rotation on particle motion near the surface 7.3 Fixed-axis rotation 7.4 Application of d'Alembert's principle 7.5 Gyroscopic effects 7.6 Intrinsic equations of the gyroscope 7.7 Description of spatial position: Euler's angular coordinates Chapter VIII. The principle of virtual work 8.1 Work, energy, and equilibrium 8.2 Equilibrium of a particle 8.3 Equilibrium of systems; the rigid body 8.4 Real systems; potential energy 8.5 Stability of equilibrium 8.6 Summary Chapter IX. Elements of the theory of mechanical vibrations 9.1 Introduction 9.2 Free vibrations of a simple mechanical system 9.3 Effect of a disturbing force 9.4 Effect of a Harmonic disturbing force 9.5 Multiple-degree-of-freedom mechanical systems 9.6 The analogies between electrical and mechanical vibrations Appendix I. Vector algebra AI.1 Scalar and vector quantities AI.2 Vector addition AI.3 Unit vectors AI.4 The Scalar product AI.5 The vector product AI.6 Triple products Appendix II. Properties of the inertia matrix AII.1 The definition of the inertia matrix AII.2 The parallel-axis transfer theorems AII.3 The rotation-of-axis transfer theorems AII.4 Further comments on the determination of the inertia matrix AII.5 Summary AII.6 Inertia properties of uniform bodies Index