[isentrop1c]

The analogy with physics and basically differential equations brings in familiar concepts from the "spherical cow in vacuum" world. If we wanna go technical, then acceleration too does not matter, cause jerk (acceleration of acceleration) matters even more. We could keep going deeper and deeper into derivatives at no gain. You can introduce mass, air resistance and whatever you want, but at the end of the day this is all just an analogy. Getting into technicalities of jargon has no practical benefit.

When people say "velocity" they actually refer to all the "derivatives". Just like when I say my car faster, well it is both faster and accelerates faster and all of those things. A Tesla is faster than a normal bicycle. Faster and "velocity" have mental association and that's all it matters. Changing a the term from "velocity" to "acceleration" and whatnot just changes the label, not practical meaning and what people want to convey.

[tgv]

As if acceleration doesn't have a direction. And how many dimensions does software development have, anyway? Replacing one analogy (distance) by another (mass) isn't going to help.

[mansoon]

You _can_ actually do this, but you'll end up insane, and ranting about god.

[Groxx]

It only looks like that if you're not observing the math from all four Earth rotations simultaneously, i.e. from the four corners of the time cube.

[mark254]

Wouldn't a (3-D) cube have eight corners?

And 3 length dimensions plus time gives a hypercube, with 16 corners.

For 11 dimensions, 2048 corners... for 26, 2^26 ;)

[mathgeek]

Good discussion on this at https://old.reddit.com/r/askmath/comments/10a2xmc/do_corners...

One of the requirements is that you have to clearly define whether your n-dimensional object is a solid.

[inkcapmushroom]

You should instead try some belly-button logic.

[aatd86]

For some things, your nth derivative can very rapidly be 0.

There might not be an acceleration of acceleration... Etc.

So "all the derivatives" doesn't make sense.

Matter is limited by the celerity of light in a vacuum after all...

[green_on_black]

Minor nitpick: we typically just need 2 derivatives in the physical world.

[atoav]

The higher derivatives of position are actually used in engineering, see: https://en.m.wikipedia.org/wiki/Jerk_(physics)

They typically play a role if you care about how smooth the transitions between two accelerations are (e.g. vehicles)

Similarly designers and engineers look at derivatives of curvature (1/radius) if they want to achieve smooth transitions between curved surfaces (e.g. car bodies).

[kfarr]

Agreed, you can really identify jerk motions in vehicles. But snap, crackle, pop? Seems almost like a joke at that point

[HPsquared]

If you're controlling a quadcopter, one limiting factor is how fast the rotors can accelerate/decelerate.

That is, the derivative of rotor thrust.

That is, the derivative of angular acceleration of the vehicle.

That is, the third derivative of the angle of the vehicle.

That is, the third derivative of the horizontal thrust of the vehicle.

That is, the third derivative of the horizontal acceleration of the vehicle.

That is, the 5th derivative of position.

[atoav]

Cannot speak about motion, but in surface continuity you will also look at higher "derivatives" if you want really really smooth transfers between two curves. So you make the transition of the curvature comb of a curve's curvature comb tangetial or so. There they just call the transitions g0, g1, g2, g3, g4 and so on.

I cannot judge whether snap, crackle and pop are things people actually use when they talk about those derivatives in motion.

[kqr]

I suspect it's not really about transitions between accelerations, but rather sudden changes in force.

[atoav]

Exactly, in the end you want smooth motion because of the resulting forces.

But since F = m×a and mass is typically something you cannot dynamically change on the fly, acceleration must do.

[QuadmasterXLII]

When hovering a helicopter, your stick controls the fourth or fifth derivative of position, depending on rotorhead design