Third order time derivative of displacement

[janakiraman]

Hi i was just wondering why do we stop with only the second order derivative of displacement which is the acceleration. I was wondering if there is no scenario in the world where we would need the third order time derivative which might talk about how the acceleration varies with respect to time? Also can it have any physical significance? I was just wondering about it.

 

[atyy]

If the acceleration a(t) is changing with time, then d(a)/dt will tell you the rate of change of acceleration. If da(t)/dt=0, then you know the acceleration has reached a maximum or minimum or a point of inflexion, and you have to examine d²a/dt² and possibly higher order derivatives to determine what is going on.

The point about Newton's second law is that since force changes acceleration, we will be able to calculate all higher order derivatives if we know the force, the initial position and the initial velocity. This assumes that the force itself doesn't depend on derivatives of position higher than second order. Of the forces I know abobut, magnetism and drag contain only first order derivatives of position.

 

[Defennder]

There's a concept of jerk related to the derivative of the acceleration.

 

[Monocles]

You can have as many derivatives of displacement as you like, and it would still have physical significance. The derivative of jerk with respect to time is called jounce. Beyond that nothing really has a widely accepted name (and jounce is iffy), because it is used so rarely.

 

[arildno]

We are sensitive to sudden changes in the force acting upon us, in that it is less stressful in a mental state to be subject to a strong, yet stable force than with a swiftly changing force.

That is, jerky motion doesn't feel good for us.


Therefore, engineer will try to "cushion" the effect of jerks, for example at how we are to cure highways and railroads etc.

 

[Andy Resnick]

I think the OP raises an interesting question, one I have heard before without a satisfactory answer, which is "Why are the essential equations of Physics 2-nd order differential equations?"

 

[Ben Niehoff]

I think the OP raises an interesting question, one I have heard before without a satisfactory answer, which is "Why are the essential equations of Physics 2-nd order differential equations?"

Time-reversal symmetry demands that they at least be equations involving only even-order derivatives, of which the second-order type are the simplest.

Note that equations with dissipative losses have first-order terms and are therefore non-symmetric with respect to time reversal. However, models for dissipative losses are always aggregate approximations; describing an exact model of friction, for example, would involve simply doing reversible dynamics on a system of very many small particles. Then the thermodynamic limit can be applied, and it is from there that we get time asymmetry.

Of course, this still doesn't completely answer the question, because one might ask, why not fourth- or sixth-order equations? The best answer I can think of is that science starts with simple models before moving to more complex ones, and second-order equations have been very accurate thus far.

 

[rcgldr]

Racing games include "jerk" calculations to model reactions by the suspension and tires of a car. I assume most real world movement control applications take "jerk" into account. So although not done often in a class room situation, 3rd order stuff is done in the real world in some areas of physics.

 

[Tac-Tics]

Time-reversal symmetry demands that they at least be equations involving only even-order derivatives, of which the second-order type are the simplest.

This is an interesting notion. Could you indulge me and give me a concrete example of a 2nd order system being time-reversible? In other words, can you elaborate what exactly you mean by time-reversible in this instance?

 

[Redbelly98]

Time-reversal symmetry demands that they at least be equations involving only even-order derivatives, of which the second-order type are the simplest.

But aren't Maxwell's Equations and Schrödinger's Equation 1st order?

 

[D H]

This is an interesting notion. Could you indulge me and give me a concrete example of a 2nd order system being time-reversible? In other words, can you elaborate what exactly you mean by time-reversible in this instance?

Any conservative force is time reversible. Gravity, for example. Given a time series of positions of a satellite orbiting the Earth well above the Earth's atmosphere, there is no way to tell whether those data are arranged with time going forward or backward.