4 ms·

4, 5, and 6 also exist (but to my understanding aren't really used): https://en.wikipedia.org/wiki/Fourth,_fifth,_and_sixth_derivatives_of_position https://en.w

• bigdict 4y ago
  Infinitely many exist if the function is infinitely differentiable (aka smooth).
• Thrymr 4y ago
  They mostly exist so they can be called "snap", "crackle", and "pop". https://web.archive.org/web/20180626030437/https://info.aiaa.org/Regions/Western/Orange_County/Newsletters/Presentations%20Posted%20by%20Enrique%20P.%20Castro/AIAAOC_SnapCracklePop_docx.pdf https://web.archive.org/web/20180626030437/https://info.aiaa...
• gojomo 4y ago
  I believe 4th (& possibly higher) is relevant in aeronautics/astronautics and robotics.
• 532nm 4y ago
  The 4th derivative is quite important for good motion control where it is usually called 'snap'. Specifically, it is relevant both for feedforward control design [1] and trajectory planning [2]. As shown in the latter, it is advantageous to design trajectories based on segments of constant snap. Consequently, also including 'snap' in the feedforward signals makes the achieved position profiles notably smoother. [1] "Control for precision mechatronics" https://doi.org/10.1007/978-3-030-44184-5_100044 https://doi.org/10.1007/978-3-030-44184-5_100044 [2] "Trajectory planning and feedforward design for electromechanical motion systems" https://doi.org/10.1016/j.conengprac.2004.02.010 https://doi.org/10.1016/j.conengprac.2004.02.010