Demonstration of time dilation using the centripetal acceleration of a clock

A mathematical demonstration is made to derive the inverse form of the Lorentz factor using as a tool the centripetal acceleration of a clock hand. When a resistance is applied against the motion of a clock hand, the centripetal acceleration decreases. The ratio between the final centripetal acceleration of the clock hand and its initial centripetal acceleration gives a ratio between two squared velocities. By squaring root this ratio, we obtain the equivalent form of the inverted Lorentz factor.

New Modeling of Steady-State Modes of Complex Electrical Grids of Power Systems

Classical methods for modeling the steady-state modes of complex electrical networks and systems are based on the application of nonlinear node equations. Nonlinear equations are solved by iterative methods, which are connected by known difficulties. To a certain extent, these difficulties can be weakened by applying topological methods. In this paper, we outline the theoretical foundations for the formation of the inverse form of nodal stress equations based on the topology of electrical networks and systems. A new topological method for calculating the distribution coefficients of node currents is proposed based on all possible trees of a directed graph of a complex electrical network. A complex program for calculating current distribution coefficients and forming steady-state parameters in the MATLAB environment has been developed.

Calculations of the complex network’s steady-state modes by brining it to equivalent open

The paper considers the development of the idea of diakoptics as applied to the calculation of the steady-state modes of energy system’s complex electrical networks. The well-known goal of diakoptics is to obtain the equations of state for the dedicated part of the system, the study of which is much simpler than the study of the initial system and can be achieved by improving its steady state equations. Technique for dividing a complex-closed system into a set of uncomplicated subsystems was developed based on the inverse form of nodal equations. Analytic expressions for the intersection circuits obtained based on identical equality of voltage at the nodes of the system division into subsystems are proposed. Using the example of 110kV network calculation, the technique for determining the matrixes of generalized parameters of the dedicated subsystems, the sizes of which depend on the number of their broken link is shown. Analytical determination of the equality condition of the voltage of subsystems intersections nodes, allowed analyzing a complex closed network by bringing it to an equivalent open.