The motion of a ball on a grassy lawn

The motion of a ball of constant spherical shape on a grassy lawn represented by a set of deformable rods with one end rigidly attached to a plane, while the other end is free and can contact the ball, is investigated. The contact area on the ball surface is represented by a spherical sector, whose dimensions and location on the ball surface depend on the position of the centre of the ball and its orientation. The projection of the contact area onto the plane is a circle, whose centre and radius vary as the centre of the ball moves. When the rods come into contact with the ball, they experience longitudinal and flexural strains, as well as impact actions on the boundary of the contact area. The translational–rotational motion of a ball on a lawn of rods without friction, as well as motion with viscous friction at the points of contact of the ends of the rods with the ball, is considered.