2021/05/15 by Zofia Wróblewska, Wróblewska, Zofia, Piotr Kowalczyk +3
Engineering · Physics and Astronomy · #34C20 #34D05 #37N25 #70K20 #70K42 #70K50 #70K60 #Dynamical Systems (math.DS) #Evacuation and Crowd Dynamics #Experimental and Theoretical Physics Studies #FOS: Mathematics #Sports Dynamics and Biomechanics
paper · pdf · doi:10.48550/arxiv.2105.07188
openalex publication_date 2021/05/15 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
We consider a classical spring-mass model of human running which is built upon an inverted elastic pendulum. Based on our previous results concerning asymptotic solutions for large spring constant (or small angle of attack), we construct analytical approximations of solutions in the considered model. The model itself consists of two sets of differential equations - one set describes the motion of the centre of mass of a runner in contact with the ground (support phase), and the second set describes the phase of no contact with the ground (flight phase). By appropriately concatenating asymptotic solutions for the two phases we are able to reduce the dynamics to a one-dimensional apex to apex return map. We find sufficient conditions for this map to have a unique stable fixed point. By numerical continuation of fixed points with respect to energy, we find a transcritical bifurcation in our model system.