Dynamics of a Partially Full Cylinder Containing a Magnetic Liquid in a Magnetic Field

Abstract

This study is concerned with the transient motion of an infinitely long thin-walled circular cylinder partially filled with a magnetic liquid under magnetic and nonmagnetic forces. Starting from rest the cylinder is constrained to roll without slipping on a plane surface while the contained fluid with a rectangular free surface is simultaneously subjected to a magnetic field parallel to the plane by activating a magnet located ahead of the cylinder. The nonmagnetic force on the cylinder and its contents is provided by the gravity. Assuming negligible viscous dissipation Lagrange’s equations of motion are derived and solved to obtain the motion of the cylinder and the liquid subsequent to the application of the magnetic field. Results are presented in a nondimensional form for motion on horizontal and inclined planes under different magnetic strengths.