Beyond velocity and acceleration: jerk, snap and higher derivatives (2016)
Higher-order derivatives of motion—jerk, snap and beyond—are usually treated as mathematical curiosities, yet engineers note they play a crucial role in real systems from elevators, trains and roller coasters to robots, vehicles and missile guidance. Contributors argue that controlling rapid changes in acceleration greatly affects passenger comfort, vibration, wear and safety, while others question how often derivatives beyond jerk are practically useful and whether naming them adds value over treating them as generic higher-order terms.
Hierarchy and terminology
- Discussion centers on the derivative chain: position → velocity → acceleration → jerk → snap → crackle → pop → higher orders.
- Several comments note jerk is intuitive (change in acceleration), while snap and above feel harder to reason about and are rarely named in education.
- Some question the value of naming beyond “n‑th derivative” versus using special terms.
Physical meaning and real-world relevance
- Multiple commenters affirm jerk is very noticeable: sudden changes in acceleration cause discomfort, seasickness, and the “drivers-ed stop” feeling.
- Electric vehicles and trolleybuses are cited as having high jerk because torque can change quickly, making starts and stops harsh for standing passengers.
- Higher derivatives (snap, etc.) are acknowledged as existing but their distinct perceptual or design importance is less clear or “unclear.”
Vehicle comfort, tracks, and rides
- Road and rail design use smooth curvature transitions (e.g., Euler / clothoid spirals) to limit jerk entering/exiting curves, improving comfort and safety.
- Roller coasters and lifts/elevators explicitly manage jerk to control rider sensation; preferences for “gut-feel” vs smooth rides reportedly vary by region and customer.
- Train engineering and automotive suspension/braking systems are said to account for jerk to reduce vibrations, wear, and passenger discomfort.
Engineering, control, and simulation
- Jerk-limited profiles are used in robotics, CNC/grinding machines, 3D printers, and self‑driving cars to avoid oscillations, reduce fatigue, and smooth motion.
- Multi-body simulations model displacement/velocity/acceleration; jerk and above are often inferred for vibration and durability analysis.
- Other cited uses: N‑body simulations, missile/inertial navigation (with Kalman filters), Apollo lunar landing guidance, social media trend “jerk” to detect sudden boosts from influencers.
Skepticism and debate
- Some argue higher derivatives add little beyond mathematical convenience; others counter with practical examples (vibration, comfort, wear).
- Debate over “speed kills” vs acceleration vs jerk: consensus in thread leans toward acceleration (force) determining injury, with jerk important for comfort and whiplash-like effects.
- There is discussion on whether acceleration can be truly discontinuous in reality; opinions differ, often invoking scale (macroscopic vs microscopic).
Integrals and conceptual notes
- Time-integrals of position (absement and higher) are mentioned in control (integral of error over time) and flow/valve examples.
- Several comments note that people often know the concepts (jerk, integral error) long before learning these specific terms.