Investigation of Systems of Differential Equations with Delays and Constraints Imposed on the Derivatives of Solutions

Law of universal gravitation with finite velocity of gravity and mathematical model of motion of a finite number of material points

“…Note that to use formulas (2) and (4), information on vector functions r 1 (t) and r 2 (t) and scalar functions τ 2,1 (t) and τ 1,2 (t) are needed. These functions can be found using differential equations with a deviating argument, which describe the motion of points M 1 and M 2 , and are obtained using Newton's second law (see [8]).…”

“…When finding the trajectories of movement of points M i , i = 1, n, it is necessary to use, in addition to the equations of system (8), also initial or boundary conditions (see [6], [8], [9]). System (8), together with these conditions, is a mathematical model of the movement of points M i , i = 1, n, that takes into account the finiteness of the speed of gravity.…”

“…Obviously, system (8), taking into account the initial conditions, can be used as a mathematical model of a stellar system with n − 1 planets with masses m i , i = 2, n, that move in a force field generated by a star with mass m 1 and planets.…”

“…it follows that even if the complexity of the equations of system (8) is not taken into account, studying system (8) at large n is a more difficult task than studying system (9). Despite this, it is possible to find such properties of system (8) that are not characteristic of system (9) (see [6], [9]).…”

“…This system, together with the initial or boundary conditions considered in [9], [11] is a mathematical model of the motion of two points with masses m 1 and m 2 . System (10) has been thoroughly investigated in the works [8][9][10][11][12].…”