If the scalar quantity x(t) denotes the position (or displacement) of a moving object, then Dx(t) (first order derivative) is called the velocity and D^2 x(t) (second order derivative) is called the acceleration.
What are the physical names and physical significance of third order, fourth order and higher order derivatives of position? In some papers and books on chaotic systems, the word 'jerk" is used for third order derivative of position (jerk system) and the word 'hyperjerk' is used for fourth order or higher order derivatives of position (hyperjerk systems). Some books use the word "snap" for fourth order derivative of position. Some papers also use the word "jounce" for the fourth order derivative of position. What are the standard or accepted names for third, fourth and higher order derivatives of position? Any reference please!
"Higher derivatives of position are related to "generalized curvatures". In 3D, for instance, the derivative of acceleration is secretly related to the torsion of a curve. The hint is the Frenet-Serret (binormal, normal, tangent) triplet or the so-called repere mobile (a la Cartan). A higher dimensional extension of this moving reference frame does exist for higher derivatives. So, higher order derivatives can be mathematically imagined to be different classes of "classical curvatures". For instance, the sign of f''(0) is related to the maximum/minimum character of f'(0)=0. Usually, people work with theories in which only "curvature" matters and torsion is usually neglected. It happens with general relativity, but some theories include torsion terms. Fluid dynamics, indeed, relates torsion to vorticity/vortex lines."
see, http://physics.stackexchange.com/questions/45517/physical-intuition-for-higher-order-derivatives
You will find some explanations in WIKI.
http://en.wikipedia.org/wiki/Jerk_(physics).
I don´t know physical names, but I´m not really a specialist.
Thanks for a very useful link - Wiki explains it beautifully!
"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 (not to talk about a collision!) lets the body whip forward faster than the achieved acceleration value alone would accomplish, but this is not apt to an experiment.
- A highly reproducible experiment to demonstrate jerk is as follows: Brake a car starting at a modest speed in two different ways:
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."
http://en.wikipedia.org/wiki/Jerk_%28physics%29
"Higher derivatives of position are related to "generalized curvatures". In 3D, for instance, the derivative of acceleration is secretly related to the torsion of a curve. The hint is the Frenet-Serret (binormal, normal, tangent) triplet or the so-called repere mobile (a la Cartan). A higher dimensional extension of this moving reference frame does exist for higher derivatives. So, higher order derivatives can be mathematically imagined to be different classes of "classical curvatures". For instance, the sign of f''(0) is related to the maximum/minimum character of f'(0)=0. Usually, people work with theories in which only "curvature" matters and torsion is usually neglected. It happens with general relativity, but some theories include torsion terms. Fluid dynamics, indeed, relates torsion to vorticity/vortex lines."
see, http://physics.stackexchange.com/questions/45517/physical-intuition-for-higher-order-derivatives
Dear friends, there are some names which I was not aware of (greater order than two!).
d3x/dt3 is jerk (also known as jolt, surge and lurch)
d4x/dt4 is jounce...
5th and beyond: Higher-order derivatives are given in the second article:
3 jerk m·s-3 rate of change of acceleration
4 jounce (snap) m·s-4 rate of change of jerk
5 crackle m·s-5 rate of change of jounce
6 pop m·s-6 rate of change of crackle
7 lock m·s-7 rate of change of pop
8 drop m·s-8 rate of change of lock
http://math.stackexchange.com/questions/143826/names-of-higher-order-derivatives
http://wearcam.org/absement/Derivatives_of_displacement.htm
Dear Prof. Ljubomir Jacić :
Thanks for a great reply.. but when I checked with Physics friends, many were not aware of name of third order derivative even, let alone names of higher order derivatives of position.
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