Intro
The Review on the Textbook of the Editor of the Series "Foundations of Engineering Mechanics" of Springer Publishing
Introduction to the Second Volume
Contents
Part III Dynamics. Some Applied Problems of Rational Mechanics
1 Stability of Motion
1 Differential Equations of Disturbed Motion
2 The Direct Lyapunov Method
3 Stability of Equilibrium and Stationary Motions of Conservative Systems
4 Thompson and Tait's Theorems
5 Study of the Stability from the Linear Approximation
6 Stability of Periodic Solutions from Consideration of the Linear Approximation

7 Oscillations of a Pendulum with a Vibrating Suspension Point. The Mathieu Equation
2 Nonlinear Oscillations
1 Basic Properties of Nonlinear Systems
2 Particular Cases of Nonlinear Oscillations
3 Using Gauss' Principle in Searching Approximate Solutions of Equations of Nonlinear Oscillations. The Bubnov-Galerkin Method
4 The Small-Parameter Method
5 The Krylov-Bogolyubov Method
6 The Method of Direct Separation of Motions
7 The Two-Scale Expansion Method
8 The Duffing Equation and Strange Attractor
3 Dynamics and Statics of the Stewart Platform

1 Problem Formulation and Kinematics of the Stewart Platform
2 Differential Equations of Motion of the Loaded Stewart Platform
3 The Effect of the Inertia and Weight of the Pneumatic Cylinders
4 Feedback Construction. Motion Stabilization for a Stewart Platform
5 Linearization of the Platform Motion Equations
6 Workspaces of A Stewart Platform in the Six-Dimensional Space of Generalized Coordinates
7 Problem Formulation and Coordinate Systems
8 Formulas for Transitions Between Coordinate Frames
9 Solution of the Direct Dynamics Problem

10 Solution of the Inverse Dynamics Problem
11 Vertical Oscillations of the Platform
12 On Instability of the Solution of the Inverse Dynamics Problem for the Stewart Platform. Introduction of Feedbacks
13 Kinematics of a Three-Rod Stewart Platform
14 Dynamics Equations for a Three-Rod Platform
15 Stabilization of Equilibrium of the Horizontal Position of the Platform
16 A Numerical Example
4 Vibrations and Autobalancing of Rotor Systems
1 Forced and Self-excited Oscillations of a Rotor with an Isotropic Viscoelastic Shaft

2 Forced and Self-excited Oscillations of a Rotor with an Orthotropic Viscoelastic Shaft
3 Automatic Balancing of a Statically Unbalanced Rotor
4 Automatic Balancing of a Jeffcott Rotor with an Orthotropic Elastic Shaft
5 Effect of Design Imperfection of the Automatic Ball Balancer
5 Elements of the Motion Control
1 Statements of Optimal Control Problems
2 Solving the Optimal Control Problem by Methods of the Classical Variational Calculus. The Pontryagin Maximum Principle
3 Boundary Conditions
4 Solving the Time-Optimal Problem Using the Pontryagin Maximum Principle