Resources

Potential Scenario

2014-Brun-EtAl-An introduction to the mechanics of the lasso

Author(s): Pierre-Thomas, Brun

NA

Keywords: bifurcation motion lasso rod model rodeo

173 total view(s), 43 download(s)

Abstract

Resource Image Here, we study the mechanics of the simplest rope trick, the Flat Loop, in which the rope is driven by the steady circular motion of the roper’s hand in a horizontal plane.

Citation

Researchers should cite this work as follows:

Article Context

Resource Type
Differential Equation Type
Technique
Qualitative Analysis
Application Area
Course
Course Level
Lesson Length
Technology
Approach
Skills

Description

Brun, Pierre-Thomas, Neil Ribe, and Basile Audoly. 2014. An introduction to the mechanics of the lasso. Proc. R. Soc. A 470. 18 pp.

See https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2014.0512 . Accessed 30 March 2023.


Abstract: Trick roping evolved from humble origins as a cattle catching tool into a sport that delights audiences all over the world with its complex patterns or ‘tricks’. Its fundamental tool is the lasso, formed by passing one end of a rope through a small loop (the honda) at the other end. Here, we study the mechanics of the simplest rope trick, the Flat Loop, in which the rope is driven by the steady circular motion of the roper’s hand in a horizontal plane. We first consider the case of a fixed (non-sliding) honda. Noting that the rope’s shape is steady in the reference frame rotating with the hand, we analyse a string model in which line tension is balanced by the centrifugal force and the rope’s weight. We use numerical continuation to classify the steadily rotating solutions in a bifurcation diagram and analyse their stability. In addition to Flat Loops, we find planar ‘coat-hanger’ solutions, and whirling modes in which the loop collapses onto itself. Next, we treat the more general case of a honda that can slide due to a finite coefficient of friction of the rope on itself. Using matched asymptotic expansions, we resolve the shape of the rope in the boundary layer near the honda where the rope’s bending stiffness cannot be neglected. We use this solution to derive a macroscopic criterion for the sliding of the honda in terms of the microscopic Coulomb static friction criterion. Our predictions agree well with rapidcamera observations of a professional trick roper and with laboratory experiments using a ‘robo-cowboy’.


Keywords: lasso, differential equation, model, motion, rod model, bifurcation, stability

Article Files

Authors

Author(s): Pierre-Thomas, Brun

NA

Comments

Comments

There are no comments on this resource.