# 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.
References in periodicals archive ?
Figure 5 shows periodic motions when the in-plane load [P.sub.1] = -260 Pa.
Since we can control the responses of the system from the chaotic motions to the periodic motions by changing the perturbation rotating speed, we can control the large amplitude nonlinear vibrations of the blade.
The fact that the Lyapunov dimension is an integer means that the system has periodic motion. When parameter [OMEGA] increases beyond the bifurcation point (such as when [OMEGA] = 7.964 rad/s), the Lyapunov exponents are [[lambda].sub.1] = 0.0054396 and [[Lambda].sub.2] = -0.092153, and the Lyapunov dimension is [d.sub.L] = 1.059.
The Second Case Periodic Motion. For the gear transmission system, the second case periodic motion that corresponds to the collision state of the gear can be divided into two cases: single-sided impact periodic motions and double-sided impact periodic motions.
Gegg, "On the mechanism of stick and non-stick periodic motion in a periodically forced, linear oscillator with dry friction," ASME Journal of Vibration and Acoustics, vol.
The Lorenz-Stenflo system has many dynamical behaviors that are one chaotic motion and six different periodic motions as shown in Figure 1.
At the same time, theory fixed point of the n - 1 periodic motion is given by
It is also found that the system enters into periodic motion from chaotic motion when the piezoelectric parameter [[alpha].sub.25] increases from 1.0 to 2.0.
As can be seen from Figure 4(a), the top Lyapunov exponent turns out to be [[lambda].sub.1] = -0.052549, which is negative, and the periodic motion of the system can be detected as presented in Figure 4(d).
In , Hartog initially made an investigation on the periodic motion of the forced linear oscillator with Coulomb and viscous damping.
The bifurcation results show that the system behaves as 1T-periodic motion at low mesh frequency and the periodic motion persists until [[omega].sub.h] > 0.425.

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