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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 angle θ which appears in the eigenvalue expression corresponds to the angle of the Euler axis and angle representation. The eigenvector corresponding to the eigenvalue of 1 is the accompanying Euler axis, since the axis is the only (nonzero) vector which remains unchanged by left-multiplying (rotating) it with the rotation matrix.
The Jeffcott rotor (named after Henry Homan Jeffcott), also known as the de Laval rotor in Europe, is a simplified lumped parameter model used to solve these equations. A Jeffcott rotor consists of a flexible, massless, uniform shaft mounted on two flexible bearings equidistant from a massive disk rigidly attached to the shaft. The simplest ...
In classical mechanics, Euler's rotation equations are a vectorial quasilinear first-order ordinary differential equation describing the rotation of a rigid body, using a rotating reference frame with angular velocity ω whose axes are fixed to the body. They are named in honour of Leonhard Euler. Their general vector form is
In rotordynamics, the rigid rotor is a mechanical model of rotating systems. An arbitrary rigid rotor is a 3-dimensional rigid object, such as a top. To orient such an object in space requires three angles, known as Euler angles. A special rigid rotor is the linear rotor requiring only two angles to describe, for example of a diatomic molecule.
In physics, angular velocity (symbol ω or , the lowercase Greek letter omega), also known as angular frequency vector, [1] is a pseudovector representation of how the angular position or orientation of an object changes with time, i.e. how quickly an object rotates (spins or revolves) around an axis of rotation and how fast the axis itself changes direction.
An early example of electromagnetic rotation was the first rotary machine built by Ányos Jedlik with electromagnets and a commutator, in 1826-27. [2] Other pioneers in the field of electricity include Hippolyte Pixii who built an alternating current generator in 1832, and William Ritchie's construction of an electromagnetic generator with four rotor coils, a commutator and brushes, also in 1832.
Specifically, the first angle moves the line of nodes around the external axis z, the second rotates around the line of nodes and the third is an intrinsic rotation (a spin) around an axis fixed in the body that moves. Euler angles are typically denoted as α, β, γ, or φ, θ, ψ. This presentation is convenient only for rotations about a ...