5 ms·

What comes after jerk? Also it’s weird to think velocity has inertia but acceleration doesn’t.

• deleted 4y ago
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• raphlinus 4y ago
  After jerk come snap, crackle, and pop. These are rarely used in practice, but I believe snap (the 4th derivative) correlates with noise in high speed trains, so it's worth optimizing railroad tracks to keep snap (and of course jerk) low. This is one reason why polynomial spirals (Spiro curves) can be great tools for representing trackways or road centerlines; with G4 continuity, snap is continuous which means crackle is finite. Also see this paper[1] (also cited by 'jjgreen elsewhere in this thread) which discusses the perception of higher derivatives in the context of roller coaster rides. [1]: https://iopscience.iop.org/article/10.1088/0143-0807/37/6/065008 https://iopscience.iop.org/article/10.1088/0143-0807/37/6/06...
• kaoD 4y ago
  Your inertia comment kept me (over)thinking for a while. So what is inertia, and what makes it interesting on its own? I guess we could describe it as v(t) = v(t - d) if a(t - d) = 0 for small d (velocity remains constant unless a force, i.e. acceleration, is applied) but this seems to be a bit self referential since it's just a longer way to say a(t) is v'(t). What makes inertia interesting compared to other derivatives? Isn't acceleration "inertial" wrt jerk by definition? Or rather, any derivable function is "inertial" wrt to its derivative. Even if we had velocity change without external forces we'd just introduce a "phantom force" like gravity to make it all work nicely. Is inertia as a concept just an artifact of classical physics being framed in terms of position and forces?