Offers on cooperation is may direct on E-mail: svyatskov-n@inbox.ru; nit21-eng@yandex.ru

APPLICATIONS of the BASIC EQUATION

Applications of this problem may be:
– Curves with a point of return (a brachistochrone, Nail parabola end etc.);
– Finding an optimal shape of a body in hypersonic flow near a point of singularity;
– Dynamics of the body with variable mass in the case of zero initial conditions;
– The management of a rotation of a shaft with a following condition: its radius many times less than its length;
– Transport mechanisms in the ocean (the management of movement of the collector of a plankton in the case of zero initial conditions and etc.);

BRIEF SURVEY of MY MOST IMPORTANT RESEARCH RESULTS and RESEARCH PLANS
I. Mathematics.
I.1. Continuity.
I.1.1. Calculus of variations.
I.1.2. Connection with the Theory Singularity Disturbed Problems.
I.1.3. Curves with a point of return (a brachistochrone, Nail parabola end etc.).
I.2. Discreteness.
I.2.1. Homomorphism.
I.2.2. Algebra equation structure.
I.2.3. Group analysis.

II. Technics.
II.1. Theoretical Mechanics.
II.1.1. Straight line movement of the body with variable mass.
II.1.2. Theorem of Change of the Kinetic Moment of Mechanical System with the Variable Moment of Inertia.
II.2. Applications.
II.2.1. Calculation for optimal shape of a body in hypersonic flow near a singular point.
II.2.2. Movement of the body with variable mass in the case of zero initial conditions.
II.2.3. Rotary Movement of a Solid Body with the Variable Moment of Inertia.