Asymptotic Solution of a Boundary Value Problem for a Spring–Mass Model of Legged Locomotion
Hanna Okrasińska-Płociniczak , Łukasz Płociniczak
AbstractRunning is the basic mode of fast locomotion for legged animals. One of the most successful mathematical descriptions of this gait is the so-called spring–mass model constructed upon an inverted elastic pendulum. In the description of the grounded phase of the step, an interesting boundary value problem arises where one has to determine the leg stiffness. In this paper, we find asymptotic expansions of the stiffness. These are conducted perturbatively: once with respect to small angles of attack, and once for large velocities. Our findings are in agreement with previous results and numerical simulations. In particular, we show that the leg stiffness is inversely proportional to the square of the attack angle for its small values, and proportional to the velocity for large speeds. We give exact asymptotic formulas to several orders and conclude the paper with a numerical verification.
|Journal series||Journal of Nonlinear Science, ISSN 0938-8974, e-ISSN 1432-1467, (N/A 100 pkt)|
|Publication size in sheets||0.85|
|Keywords in English||Singular perturbation theory, Boundary value problem, Poincare-Lindstedt series, Elastic pendulum, Running, Spring-mass model|
|ASJC Classification||; ;|
|License||Journal (articles only); published final; ; with publication|
|Score||= 100.0, 14-11-2020, ArticleFromJournal|
|Publication indicators||= 0; : 2018 = 1.368; : 2019 = 2.104 (2) - 2019=2.199 (5)|
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.