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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.
The method removes secular terms—terms growing without bound—arising in the straightforward application of perturbation theory to weakly nonlinear problems with finite oscillatory solutions. [1] [2] The method is named after Henri Poincaré, [3] and Anders Lindstedt. [4]
The tautochrone problem is a special case of Abel's mechanical problem when () is a constant. Abel's solution begins with the principle of conservation of energy – since the particle is frictionless, and thus loses no energy to heat , its kinetic energy at any point is exactly equal to the difference in gravitational potential energy from its ...
The finite point method (FPM) is a meshfree method for solving partial differential equations (PDEs) on scattered distributions of points. The FPM was proposed in the mid-nineties in (Oñate, Idelsohn, Zienkiewicz & Taylor, 1996a), [1] (Oñate, Idelsohn, Zienkiewicz, Taylor & Sacco, 1996b) [2] and (Oñate & Idelsohn, 1998a) [3] with the purpose to facilitate the solution of problems involving ...
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 ...
Thus, solutions of the boundary value problem correspond to solutions of the following system of N equations: (;,) = (;,) = (;,) =. The central N−2 equations are the matching conditions, and the first and last equations are the conditions y(t a) = y a and y(t b) = y b from the boundary value problem. The multiple shooting method solves the ...
In mathematics, a collocation method is a method for the numerical solution of ordinary differential equations, partial differential equations and integral equations.The idea is to choose a finite-dimensional space of candidate solutions (usually polynomials up to a certain degree) and a number of points in the domain (called collocation points), and to select that solution which satisfies the ...
In applied mathematics, the finite pointset method (FPM) is a general approach for the numerical solution of problems in continuum mechanics, such as the simulation of fluid flows. In this approach the medium is represented by a finite set of points, each endowed with the relevant local properties of the medium such as density , velocity ...