periodic motion


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Periodic motion

Any motion that repeats itself identically at regular intervals. If x(t) represents the displacement of any coordinate of the system at time t, a periodic motion has the property defined by the equation below for every value of

the variable time t. The fixed time interval T between repetitions, or the duration of a cycle, is known as the period of the motion.

The motion of the escapement mechanism of a watch, the motion of the Earth about the Sun, and the more complicated motion of the crankshaft, piston rods, and pistons in an engine running at uniform speed are all examples of periodic motion.

The vibration of a piano string after it is struck is a damped periodic motion, not strictly periodic according to the definition. Although the motion very nearly repeats itself, and with a fixed repetition time, each successive cycle has a slightly smaller amplitude. See Damping, Harmonic motion, Vibration, Wave motion

periodic motion

[¦pir·ē¦äd·ik ′mō·shən]
(mechanics)
Any motion that repeats itself identically at regular intervals.
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References in periodicals archive ?
With increasing the transmission error En, the periodic motion and chaotic state present alternately in the parameter plane.
It is also interesting that the system is in the chaotic state for a small [xi] and in periodic motion at larger [xi].
Bifurcation Observation of Combining Spiral Gear Transmission Based on Parameter Domain Structure Analysis
These all indicate that the vibration response of pipe wall is a periodic motion.
The eight closed curve in s-v phase diagram and eight separate points in Poincaree section show that the response of pipe wall is the 8T periodic motion.
Nonlinear Dynamic Behavior Analysis of Pressure Thin-Wall Pipe Segment with Supported Clearance at Both Ends
Figure 6 illustrates the periodic motion observed at a flow rate of 1.
However, at the flow rates employed in this study there was no significant effect of particle size on the amplitude and the frequency of the periodic motion, at least for the sphere sizes used in this study.
Particle motion in the fountain flow region during filling of a tube with a viscoelastic fluid
It is accompanied by the retrograde free core nutation (RFCN), a small periodic motion of the Earth's axis of rotation in space.
Quasi-diurnal atmospheric and oceanic excitation of nutation
To control the ribbon's motion, the researchers display the attractor on a computer screen and select a point that corresponds to a particular type of periodic motion.
Ribbons of chaos: researchers develop a lab technique for snatching order out of chaos
1965, On the existence of almost periodic motions, Michigan Math.
Almost periodic functions with values in p-frechet spaces, 0 < p < 1
In general, the clock was one of the fundamental metaphors of the era, with the periodic motions of the heavens constituting a celestial clockwork.
Instruments and the Imagination
Periodic motions and chaos with impacting chatter and stick in a gear transmission system, International Journal of Bifurcation and Chaos 19(6): 1975-1994.
Analysis of nonlinear dynamics and chaos control in gear transmission system with stochastic perturbation
Many of the objects observed in the programs of monitoring Earth orientation from the ground are double or multiple systems, having non-negligible periodic motions.
Earth orientation parameters based on EOC-4 astrometric catalog

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