Papers › How Many Equations of Motion Describe a Moving Human?
How Many Equations of Motion Describe a Moving Human?
Gabriele De Luca, Thomas J. Lampoltshammer, Johannes Scholz
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
A human is a thing that moves in space. Like all things that move in space, we can in principle use differential equations to describe their motion as a set of functions that maps time to position (and velocity, acceleration, and so on). With inanimate objects, we can reliably predict their trajectories by using differential equations that account for up to the second-order time derivative of their position, as is commonly done in analytical mechanics. With animate objects, though, and with humans, in particular, we do not know the cardinality of the set of equations that define their trajectory. We may be tempted to think, for example, that by reason of their complexity in cognition or behaviour as compared to, say, a rock, then the motion of humans requires a more complex description than the one generally used to describe the motion of physical systems. In this paper, we examine a real-world dataset on human mobility and consider the information that is added by each (computed, but denoised) additional time derivative, and find the maximum order of derivatives of the position that, for that particular dataset, cannot be expressed as a linear transformation of the previous. In this manner, we identify the dimensionality of a minimal model that correctly describes the observed trajectories. We find that every higher-order derivative after the acceleration is linearly dependent upon one of the previous time-derivatives. This measure is robust against noise and the choice for differentiation techniques that we use to compute the time-derivatives numerically as a function of the measured position. This result imposes empirical constraints on the possible sets of differential equations that can be used to describe the kinematics of a moving human.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections