The Main Mathematical Apparatus of Vibrational Mechanics and of the Method of Direct Separation of Motions

The following sections are included:

• Preliminary Remarks

• The Initial Equation and Its Reduction to a System of Integro-differential Equations

• The Case when a Separate Equation for the Slow Component is Obtained

• The Main Assumption of Vibrational Mechanics, its Formalization and Conditions of its Fulfillment

• The Main Equation of Vibrational Mechanics. Vibrational Forces, Observers O and V

• Method of an Approximate Derivation of the Expression of Vibrational Forces and of Composing the Main Equation of Vibrational Mechanics

• Important Special Case

• On the Case of a Mechanical Systems with Constraints

• On the Simplifications of Solving Equations for the Fast Component of Motion. Purely Inertial Approximation

• Additional Remarks, Certain Generalizations

• Summary: On the Procedure of the Practical Use of the Method