Experimental investigation of the motion of a body with an axisymmetric base sliding on a rough plane

In this paper we investigate the dynamics of a body with a flat base (cylinder) sliding on a horizontal rough plane. For analysis we use two approaches. In one of the approaches using a friction machine we determine the dependence of friction force on the velocity of motion of cylinders. In the other approach using a high-speed camera for video filming and the method of presentation of trajectories on a phase plane for analysis of results, we investigate the qualitative and quantitative behavior of the motion of cylinders on a horizontal plane. We compare the results obtained with theoretical and experimental results found earlier. In addition, we give a systematic review of the well-known experimental and theoretical results in this area.

[1]  D. Dowson History of Tribology , 1979 .

[2]  V. Kozlov The problem of realizing constraints in dynamics , 1992 .

[3]  V. Kozlov On the Integration Theory of Equations of Nonholonomic Mechanics , 2005, nlin/0503027.

[4]  A. Borisov,et al.  Strange attractors in rattleback dynamics , 2003 .

[6]  A. Sarkar Friction and wear , 1980 .

[7]  Rapidly rotating sliding cylinders: Trajectories with large lateral displacements , 2002 .

[8]  On the idealization of surface of contact in form of point contact in the problem of rolling , 1966 .

[9]  H. Resal Commentarie a la theorie mathematique du jeu de billard , 2010 .

[10]  A. Borisov,et al.  The jacobi integral in nonholonomic mechanics , 2015 .

[11]  V. Ph. Zhuravlev,et al.  Global motion of the celt , 2008 .

[12]  A. Borisov,et al.  On the loss of contact of the Euler disk , 2015 .

[13]  Alexander A. Kilin,et al.  The dynamics and control of a spherical robot with an internal omniwheel platform , 2015 .

[14]  Nonlinear dynamics of the rattleback: a nonholonomic model , 2014 .

[15]  A. Malthe-Sørenssen Dynamics of Rigid Bodies , 2015 .

[16]  H. Kitchen,et al.  Comments on the Paper by , 1999 .

[17]  V. Ph. Zhuravlev,et al.  On the dynamics of the thompson top (tippe top) on the plane with real dry friction , 2005 .

[18]  A. Ruina,et al.  Planar sliding with dry friction Part 2. Dynamics of motion , 1991 .

[19]  P. V. Kharlamov A critique of some mathematical models of mechanical systems with differential constraints , 1992 .

[20]  R. Yarmukhamedov,et al.  Comments to the paper , 2010 .

[21]  G. Coriolis,et al.  Théorie mathématique des effets du jeu de billard , 1835 .

[22]  V. Zhuravlev The model of dry friction in the problem of the rolling of rigid bodies , 1998 .

[23]  B. Langerock,et al.  Dynamics of the tippe top via Routhian reduction , 2007, 0704.1221.

[24]  P. Painlevé Leçons sur le frottement , 2016 .

[25]  K. Vøyenli,et al.  On the motion of an ice hockey puck , 1985 .

[26]  Jan Awrejcewicz,et al.  Application and experimental validation of new computational models of friction forces and rolling resistance , 2015 .

[27]  A sphere rolling on a horizontal rotating plane , 1983 .

[28]  A. Kíreenkov,et al.  Experimental study of coupled two-dimensional models of sliding and spinning friction , 2010 .

[29]  A dynamically consistent model of the contact stresses in the plane motion of a rigid body , 2009 .

[30]  On the motion of a heavy body with a circular base on a horizontal plane and riddles of curling , 2012 .

[31]  Alexey V. Borisov,et al.  How to control Chaplygin’s sphere using rotors , 2012 .

[32]  On the motion of a homogeneous rotating disk along a plane in the case of combined friction , 2002 .

[33]  C. Coulomb Théorie des machines simples (Nouv. éd.) / , en ayant égard au frottement de leurs parties et à la roideur des cordages, par C.-A. Coulomb,... Nouvelle édition... , 1821 .

[34]  A. Borisov,et al.  Dynamical phenomena occurring due to phase volume compression in nonholonomic model of the rattleback , 2012 .

[35]  Guido Bartels,et al.  Frictional coupling between sliding and spinning motion. , 2003, Physical review letters.

[36]  V. Zhuravlev On the limiting accuracy of a free gyro , 2006 .

[37]  Alexey V. Borisov,et al.  The hierarchy of dynamics of a rigid body rolling without slipping and spinning on a plane and a sphere , 2013 .

[38]  V. Zhuravlev Dynamics of a heavy homogeneous ball on a rough plane , 2006 .

[39]  A. Zobova,et al.  Ball on a viscoelastic plane , 2013 .

[40]  F. P. Bowden,et al.  The Friction and Lubrication of Solids , 1964 .

[41]  R. Cross The rise and fall of spinning tops , 2013 .

[42]  Åke Björck,et al.  Numerical Methods , 1995, Handbook of Marine Craft Hydrodynamics and Motion Control.

[43]  Clifford A Frohlich What makes bowling balls hook , 2004 .

[44]  A. Markeev On the dynamics of a solid on an absolutely rough plane , 1983 .

[45]  Die Prinzipien der Mechanik in neuem Zusammenhange dargestellt, mit drei Arbeiten , 1984 .

[46]  P. Contensou Couplage entre frottement de glissement et frottement de pivotement dans la théorie de la toupie , 1963 .

[47]  H. Ziegler,et al.  Dynamics of rigid bodies and systems , 1965 .

[48]  Alexey V. Borisov,et al.  How to control the Chaplygin ball using rotors. II , 2013 .

[49]  C. Coulomb Théorie des machines simples, en ayant égard au frottement de leurs parties et a la roideur des cordages , 1968 .

[50]  O. Reynolds V. On rolling-friction , 1875, Proceedings of the Royal Society of London.

[51]  I. Neĭmark,et al.  Dynamics of Nonholonomic Systems , 1972 .

[52]  A. Borisov,et al.  The dynamics of a body with an axisymmetric base sliding on a rough plane , 2014 .

[53]  E. T. Jensen,et al.  The motion of curling rocks: Experimental investigation and semi-phenomenological description , 2004, 2112.09835.

[54]  Arend L. Schwab,et al.  Linearized dynamics equations for the balance and steer of a bicycle: a benchmark and review , 2007, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[55]  M. R. Sarkardei Towards the consistent histories approach to quantum mechanics , 2004 .