TITLE:
The Influence of the Field of Relative Inertial Forces of a Two-Mass Mechanical System as an Equivalent of Its Internal Interactions on Its Motion
AUTHORS:
Sergey V. Savel’kaev
KEYWORDS:
Two-Mass Mechanical System, Complex Motion, D’ Alembert’s Principle, Constraint Axiom for Relative Inertial Forces, Equations of Motion, Relativity of Time, Conservation of Momentum and Energy, Minimum Action
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.9,
September
20,
2026
ABSTRACT: This paper considers a mechanical system consisting of two bodies with masses
m
1
and
m
2
linked by a kinematic hinged-rod constraint in the form of a rigid straight rod
R
, allowing them to rotate both relative to each other and to their center of mass. Based on D’ Alembert’s principle formulated taking into account the constraint axiom for a constrained material point, equations of motion are derived separately for each body (
m
1
and
m
2
) and for their center of mass in the field of relative inertial forces of the diametrically opposite bodies
m
2
and
m
1
both in vacuum and in a dissipative medium. It is shown that time in the proper reference frames of these bodies flows differently than time in the center-of-mass frame, varying with the kinematic characteristics and mass ratio of the bodies. In the center-of-mass frame and the laboratory frame, time is absolute. In addition, the momentum distribution between the bodies of the closed mechanical system is analyzed, and the relationship between this distribution and its energy balance is established under various initial conditions, demonstrating that its motion in the relative inertial force field satisfies the laws of conservation of momentum and energy, as well as the principle of least action.