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Rotordynamics (or rotor dynamics) is a specialized branch of applied mechanics concerned with the behavior and diagnosis of rotating structures. It is commonly used to analyze the behavior of structures ranging from jet engines and steam turbines to auto engines and computer disk storage .
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
The Magnus effect is a phenomenon that occurs when a spinning object is moving through a fluid or gas (air). A lift force acts on the spinning object and its path may be deflected in a manner not present when it is not spinning.
The classical linear rotor consists of two point masses and (with reduced mass = +) at a distance of each other. The rotor is rigid if is independent of time. The kinematics of a linear rigid rotor is usually described by means of spherical polar coordinates, which form a coordinate system of R 3.
Rotation around a fixed axis or axial rotation is a special case of rotational motion around an axis of rotation fixed, stationary, or static in three-dimensional space.This type of motion excludes the possibility of the instantaneous axis of rotation changing its orientation and cannot describe such phenomena as wobbling or precession.
Every rotation in 3D space has a fixed axis unchanged by rotation. The rotation is completely specified by specifying the axis of rotation and the angle of rotation about that axis. Without loss of generality, this axis may be chosen as the z-axis of a Cartesian coordinate system, allowing a simpler visualization of the rotation.
A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, with an Introduction to the Problem of Three Bodies (4th ed.). New York: Dover Publications. p. 83. ISBN 978-0-521-35883-5. Routh EJ (1960). A Treatise on Dynamics of a Particle (reprint of 1898 ed.). New York: Dover Publications. pp. 230–233 (sections §356–359).
The following table refers to rotation of a rigid body about a fixed axis: is arc length, is the distance from the axis to any point, and is the tangential acceleration, which is the component of the acceleration that is parallel to the motion.