### Session G14: Invited Session: Toys and Mechanisms

11:15 AM–2:15 PM, Tuesday, March 4, 2014
Room: 301-303

Chair: James Hanna, Virginia Polytechnic Institute and State University

Abstract ID: BAPS.2014.MAR.G14.5

### Abstract: G14.00005 : The mechanics of trick roping

1:39 PM–2:15 PM

MathJax On | Off     Abstract

#### Author:

Pierre-Thomas Brun
(EPFL, LFMI)

Trick roping evolved from humble origins as a cattle-catching tool into a sport that delights audiences the world over with its complex patterns or tricks,'' such as the Merry-Go-Round , the Wedding-Ring, the Spoke-Jumping, the Texas Skip... Its implement is the lasso, a length of rope with a small loop (honda'') at one end through which the other end is passed to form a large loop. Here, we study the physics of the simplest rope trick, the Flat Loop, in which the motion of the lasso is forced by a uniform circular motion of the cowboy's/cowgirl's hand in a horizontal plane. To avoid accumulating twist in the rope, the cowboy/cowgirl rolls it between his/her thumb and forefinger while spinning it. The configuration of the rope is stationary in a reference frame that rotates with the hand. Exploiting this fact we derive a dynamical string'' model in which line tension is balanced by the centrifugal force and the rope's weight. Using a numerical continuation method, we calculate the steady shapes of a lasso with a fixed honda, examine their stability, and determine a bifurcation diagram exhibiting coat-hanger shapes and whirling modes in addition to flat loops. We then extend the model to a honda with finite sliding friction by using matched asymptotic expansions to determine the structure of the boundary layer where bending forces are significant, thereby obtaining a macroscopic criterion for frictional sliding of the honda. We compare our theoretical results with high-speed videos of a professional trick roper and experiments performed using a laboratory robo-cowboy.'' Finally, we conclude with a practical guidance on how to spin a lasso in the air based on the results of our analysis.

To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2014.MAR.G14.5