3 ms·

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

atoav 4y ago
The higher derivatives of position are actually used in engineering, see: https://en.m.wikipedia.org/wiki/Jerk_(physics) 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 4y ago
  Agreed, you can really identify jerk motions in vehicles. But snap, crackle, pop? Seems almost like a joke at that point
  - atoav 4y ago
    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.
  - HPsquared 4y ago
    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.
- kqr 4y ago
  I suspect it's not really about transitions between accelerations, but rather sudden changes in force.
  - atoav 4y ago
    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 4y ago
When hovering a helicopter, your stick controls the fourth or fifth derivative of position, depending on rotorhead design

The higher derivatives of position are actually used in engineering, see: https://en.m.wikipedia.org/wiki/Jerk_(physics) 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 4y ago
Agreed, you can really identify jerk motions in vehicles. But snap, crackle, pop? Seems almost like a joke at that point
- atoav 4y ago
  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.
- HPsquared 4y ago
  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.
kqr 4y ago
I suspect it's not really about transitions between accelerations, but rather sudden changes in force.
- atoav 4y ago
  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 4y ago

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