Foreword; Preface; Contents; Part I. The Basis of Vibrational Mechanics; Chapter 1. On Some Nonlinear Oscillatory Effects. The Main Idea of Vibrational Mechanics; 1.1 On the Effects Caused by the Action of Vibration in Nonlinear Oscillatory Systems; 1.2 The Main Idea of Vibrational Mechanics. Observer O and Observer V; Chapter 2. The Main Mathematical Apparatus of Vibrational Mechanics and of the Method of Direct Separation of Motions; 2.1 Preliminary Remarks; 2.2 The Initial Equation and Its Reduction to a System of Integro-differential Equations.

2.3 The Case When a Separate Equation for the Slow Component is Obtained2.4 The Main Assumption of Vibrational Mechanics Its Formalization and Conditions of its Fulfillment; 2.5 The Main Equation of Vibrational Mechanics. Vibrational Forces Observers O and V; 2.6 Method of an Approximate Derivation of the Expression of Vibrational Forces and of Composing the Main Equation of Vibrational Mechanics; 2.10 Additional Remarks Certain Generalizations; 2.7 Important Special Case; 2.8 On the Case of a Mechanical Systems with Constraints.

2.9 On the Simplifications of Solving Equations for the Fast Component of Motion. Purely Inertial Approximation2.11 Summary: On the Procedure of the Practical Use of the Method; Chapter 3. On Other Methods of Obtaining Expressions for the Vibrational Forces and the Main Equations of Vibrational Mechanics; 3.1 Well Known Methods; 3.2 Two Other Methods; Chapter 4. A Simplest Example: Solving the Problem about a Pendulum with a Vibrating Axis of Suspension by Different Methods of the Theory of Nonlinear Oscillations; 4.1 Preliminary Remarks; 4.2 Equation of Motion.

4.3 The Poincare-Lyapunov Method of Small Parameter4.4 The Use of Floquet-Lyapunov's Theory and of Ince-Strutt's Diagram; 4.5 Asymptotic Method; 4.6 Method of Multiple Scales; 4.7 Methods of Harmonic Balance and of Bubnov-Galerkin; 4.8 Method of Direct Separation of Motions; 4.9 Discussion; Chapter 5. Conclusion: On the Main Peculiarities and Advantages of the Approaches of Vibrational Mechanics and of the Method of Direct Separation of Motions as Compared to Other Methods of Nonlinear Mechanics; 5.1 Peculiarities and Limitations; 5.2 Advantages; 5.3 Final Remarks; References to Part 1.

Part II. Pendulum and Pendulum Systems under High-Frequency Excitation -- Non-Trivial EffectsChapter 6. Quasi-equilibrium Positions and Stationary Rotations of the Pendulums with a Periodically Vibrating Axis; 6.1 Preliminary Remarks Equation of Motion; 6.2 Regimes of Quasi-Equilibrium; 6.3 Regimes of Rotation; References; Chapter 7. Non-Trivial Effects of High-Frequency Excitation for Pendulum Systems; 7.1 Preliminary Remarks; 7.2 Chelomei's Pendulum -- Resolving a Paradox; 7.3 Nonlinear Dynamics of the Follower-Loaded Double Pendulum with Added Support-Excitation.