Beyond velocity and acceleration: jerk, snap and higher derivatives (2016)

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.