Abstract
The principle of least effort has been widely used to explain phenomena related to human behavior ranging from topics in language to those in social systems. It has precedence in the principle of least action from the Lagrangian formulation of classical mechanics. In this study, we present a model for interceptive human walking based on the least action principle. Taking inspiration from Lagrangian mechanics, a Lagrangian is defined as effort minus security, with two different specific mathematical forms. The resulting Euler–Lagrange equations are then solved to obtain the equations of motion. The model is validated using experimental data from a virtual reality crossing simulation with human participants. We thus conclude that the least action principle provides a useful tool in the study of interceptive walking.
Highlights
The principle of least effort has been widely used to explain phenomena related to human behavior ranging from topics in language to those in social systems
We first propose the Lagrangian mechanics of interceptive walking by defining a Lagrangian and solving the resulting Euler–Lagrange equation, which yields the path of stationary action
To verify the validity of each case of the model, we make a comparison with the data obtained from a virtual reality road-crossing experiment
Summary
The principle of least effort has been widely used to explain phenomena related to human behavior ranging from topics in language to those in social systems. We take this approach and propose a principle of least action, which is used for modeling human walking behavior. We first propose the Lagrangian mechanics of interceptive walking by defining a Lagrangian and solving the resulting Euler–Lagrange equation, which yields the path of stationary action.
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