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This method can be continued indefinitely in the same way, where the order-n term consists of a harmonic term + (), plus some super-harmonic terms , +, +. The coefficients of the super-harmonic terms are solved directly, and the coefficients of the harmonic term are determined by expanding down to order-(n+1), and eliminating ...
The equation describing the relative motion is known as the swing equation, which is a non-linear second order differential equation that describes the swing of the rotor of synchronous machine. The power exchange between the mechanical rotor and the electrical grid due to the rotor swing (acceleration and deceleration) is called Inertial response.
in which the last equation is referred to as the Nikolaevsky equation, named after V. N. Nikolaevsky who introudced the equation in 1989, [18] [19] [20] whereas the first two equations has been introduced by P. Rajamanickam and J. Daou in the context of transitions near tricritical points, [17] i.e., change in the sign of the fourth derivative ...
Another method, pressure-swing distillation, relies on the fact that an azeotrope is pressure dependent. An azeotrope is not a range of concentrations that cannot be distilled, but the point at which the activity coefficients of the distillates are crossing one another. If the azeotrope can be "jumped over", distillation can continue, although ...
The smaller mass, labelled m, is allowed to swing freely whereas the larger mass, M, can only move up and down. Assume the pivots to be points. The swinging Atwood's machine (SAM) is a mechanism that resembles a simple Atwood's machine except that one of the masses is allowed to swing in a two-dimensional plane, producing a dynamical system ...
For amplitudes beyond the small angle approximation, one can compute the exact period by first inverting the equation for the angular velocity obtained from the energy method , = and then integrating over one complete cycle, = (), or twice the half-cycle = (), or four times the quarter-cycle = (), which leads to = .
From the mathematical point of view the Lippmann–Schwinger equation in coordinate representation is an integral equation of Fredholm type. It can be solved by discretization . Since it is equivalent to the differential time-independent Schrödinger equation with appropriate boundary conditions, it can also be solved by numerical methods for ...
The simplest form of a group-contribution method is the determination of a component property by summing up the group contributions : [] = +.This simple form assumes that the property (normal boiling point in the example) is strictly linearly dependent on the number of groups, and additionally no interaction between groups and molecules are assumed.