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In the mathematical field of dynamical systems, a random dynamical system is a dynamical system in which the equations of motion have an element of randomness to them. Random dynamical systems are characterized by a state space S, a set of maps from S into itself that can be thought of as the set of all possible equations of motion, and a probability distribution Q on the set that represents ...
Different modelling and design criteria will affect the nature of the 'ideal' RAO curves (as plotted graphically) being sought for a particular ship: for example, an ocean cruise liner will have a considerable emphasis placed upon minimizing accelerations to ensure the comfort of the passengers, while the stability concerns for a naval warship will be concentrated upon making the ship an ...
Large vessels sometimes use electrical propulsion motors, the electrical power being provided by a diesel generator. Noise and vibration of electric motors include, besides mechanical and aerodynamic sources, an electromagnetic source due to electromagnetic forces which is responsible for the "whining noise" of the motor.
The vertical/Z axis, or yaw axis, is an imaginary line running vertically through the ship and through its centre of mass. A yaw motion is a side-to side movement of the bow and stern of the ship. The transverse/Y axis, lateral axis, or pitch axis is an imaginary line running horizontally across the ship and through the centre of mass. A pitch ...
Mathematically, random vibration is characterized as an ergodic and stationary process. A measurement of the acceleration spectral density (ASD) is the usual way to specify random vibration. The root mean square acceleration (G rms ) is the square root of the area under the ASD curve in the frequency domain.
The A4W reactor is a naval reactor used by the United States Navy to propel warships and generate onboard electricity. The A4W designation stands for: A = Aircraft carrier platform; 4 = Contractor's fourth core design generation; W = Westinghouse, the contracted designer
The original Langevin equation [1] [2] describes Brownian motion, the apparently random movement of a particle in a fluid due to collisions with the molecules of the fluid, = + (). Here, v {\displaystyle \mathbf {v} } is the velocity of the particle, λ {\displaystyle \lambda } is its damping coefficient, and m {\displaystyle m} is its mass.
This quality of unpredictability and apparent randomness led the logistic map equation to be used as a pseudo-random number generator in early computers. [ 4 ] At r = 2, the function r x ( 1 − x ) {\displaystyle rx(1-x)} intersects y = x {\displaystyle y=x} precisely at the maximum point, so convergence to the equilibrium point is on the ...