An Example. A Soccer Ball-Soccer Field System
摘要
Every day we experiment motion and shape change of continuum media, assembly of different space dimension structures, fluids, solids which exhibit numerous evolutions either particular or general: large deformations, incompressibility, cavitation, contact, surface tension, defects, dislocations,... Stretch and rotation are a common feature of these motions and phenomenons. We base a continuum mechanics predictive theory on stretch and rotation quantified by matrices. In this Chapter the motion of a point with respect to a table simple example, is sophisticated by assuming the point is a soccer-ball. The shape of the system soccer-ball soccer-field are the position of the center of mass and the rotation matrix with respect to the soccer-field. The shape change velocities are defined by the velocity of the center of mass and the angular velocity. The virtual velocities are velocities of the center of mass and angular velocities, we may think of. With the principle of virtual power they give the equations of motion. Experiment points out an internal constraint, a kinematic incompatibility: the non interpenetrability of the ball and the field. This kinematic incompatibility is taken into account by a pseudo-potential of dissipation. An example shows how sophisticated and surprising may be the motion of the ball. This chapter gives a framework for investigating the motion of intricate mechanical systems.