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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Jerk (physics) ： ウィキペディア英語版 Jerk (physics) In physics, jerk, also known as jolt, surge, or lurch, is the rate of change of acceleration; that is, the derivative of acceleration with respect to time, and as such the second derivative of velocity, or the third derivative of position. Jerk is defined by any of the following equivalent expressions: :$\backslash vec\; j(t)=\backslash frac\; =\backslash dot\; (t)=\backslash frac\; =\backslash ddot(t)=\backslash frac\; =\backslash overset(t)$ where :$\backslash vec\; a$ is acceleration, :$\backslash vec\; v$ is velocity, :$\backslash vec\; r$ is position, :$\backslash mathit$ is time. Jerk is a vector, and there is no generally used term to describe its scalar magnitude (more precisely, its norm, e.g. "speed" as the norm of the velocity vector). According to the result of dimensional analysis of jerk, (), the SI units are m/s3 (or m·s−3). There is no universal agreement on the symbol for jerk, but $j$ is commonly used. Newton's notation for the time derivative ($\backslash dot,\backslash ;\backslash ddot,\backslash ;\backslash overset$) is also applied. The fourth derivative of position, equivalent to the first derivative of jerk, is jounce. Because of involving third derivatives, in mathematics differential equations of the form :: $J\backslash left(\backslash overset,\backslash ddot,\backslash dot\; ,x\backslash right)=0$ are called ''jerk equations''. It has been shown that a jerk equation, which is equivalent to a system of three first order, ordinary, non-linear differential equations, is in a certain sense the minimal setting for solutions showing chaotic behaviour. This motivates mathematical interest in ''jerk systems''. Systems involving a fourth or higher derivative are accordingly called ''hyperjerk systems''. ==Physiological effects and human perception of physical jerk== The smooth movement and also the rest state of an alert human body is achieved by balancing the forces of several antagonistic muscles which are controlled across neural paths by the brain (for directed movement) or sometimes across reflex arcs. In balancing some given force (holding or pulling up a weight, e.g.) the postcentral gyrus establishes a control loop to achieve this equilibrium by adjusting the muscular tension according to the sensed position of the actuator. If the load changes faster than the current state of this control loop is capable of supplying a suitable, adaptive response, the balance cannot be upheld, because the tensioned muscles cannot relax or build up tension fast enough and overshoot in either direction, until the neural control loop manages to take control again. Of course the time to react is limited from below by physiological bounds and also depends on the attention level of the brain: an ''expected'' change will be stabilized faster than a ''sudden'' drop or increase of load. So passengers in transportation, who need this time to adapt to stress changes and to adjust their muscle tension, or else suffer conditions such as whiplash, can be safely subjected both only to a less than maximum acceleration, and to a less than maximum jerk,〔 so to avoid loss of control over their body motion thereby endangering their physical integrity. Even where occupant safety is not an issue, excessive jerk may result in an uncomfortable ride on elevators, trams, and the like, and engineers expend considerable design effort to minimize "jerky motion". Since forces, changing at a suitable rate in time (that is, ''suitable'' jerk) are the cause of vibrations, and vibrations significantly impair the quality of transportation, there is good reason to simply ''minimize'' jerk in transportation vehicles. As an everyday example, driving in a car can show effects of acceleration and jerk. The more experienced drivers accelerate smoothly, but beginners provide a ''jerky'' ride. * Changing gears, especially with a foot-operated clutch, offers well-known examples: although the accelerating force is bounded by the engine power, an inexperienced driver lets you experience severe jerk, because of intermittent force closure over the clutch. * High-powered sports cars offer the feeling of being pressed into the cushioning, but this is the force of the acceleration. Only in the very first moments, when the torque of the engine grows with the rotational speed, the acceleration grows remarkably and a slight whiplash effect is noticeable in the neck, mostly masked by the jerk of gear switching. * The beginning of an emergency braking lets the body whip forward faster than the achieved acceleration value alone would accomplish, and a collision does so to an even greater degree, but quantitative testing on living humans (and, for some, on animals) runs afoul of ethical concerns, with the effect that cadavers or crash test dummies must be substituted, which, of course, do not show the physiological reactions to jerk caused by an active control loop described above. * A highly reproducible experiment to demonstrate jerk is as follows: Brake a car starting at a ''modest'' speed in two different ways: *# apply a constant, modest force on the pedal till the car comes to a halt, only then release the pedal; *# apply the same, constant, modest force on the pedal, but just before the halt, reduce the force on the pedal, optimally releasing the pedal fully, exactly when the car stops. :The reason for the by far bigger jerk in the first way to brake is a ''discontinuity'' of the acceleration, which is initially at a ''constant'' value, due to the constant force on the pedal, and ''drops to zero'' immediately, when the wheels stop rotating. Note that there would be ''no jerk'' if the car started to move ''backwards'' with the same acceleration. Every experienced driver knows how to start and how to stop braking with low jerk. See also below in the motion profile, segment 7: ''Deceleration ramp-down''. For some remarks on how the human perception of various motions is organized in the proprioceptors, the vestibular organ and by visual impressions, and how to deceive it, see the article on motion simulators. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Jerk (physics)」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.