Communicated by H. NeunzertIf a ball is viewed as a rigid body, its flight in the atmosphere can be described by a system of six ordinary differential equations, which has been derived in the first part of this paper.In this following second part, the theoretical aspects such as the curvature of the orbit and certain velocity functions will be investigated in the case of the vertical angular frequency of the rotating ball, in which the differential equations reduce to a planar dynamical system. This system turns out to be not explicitly solvable.The solutions of the corresponding ordinary or boundary value problems, computed numerically, are used to treat certain problems in international ball games, for example, the maximum and minimum velocities of a volleyball service.

A model of the forces and the torque operating on a ball that is flying with rotation in the atmosphere of the Earth, and the resulting system of ordinary differential equations, are derived from mechanics and aerodynamics.The system of equations allows the theoretical aspects of the flight of a ball, such as the boundedness of its kinetic energy, the curvature of the orbit or the velocity function, to be investigated using certain transformations of the variables.The solutions of the corresponding ordinary or boundary value problems, computed numerically, are used to treat certain tasks in international ball games, for example, the maximum and minimum velocities of a volleyball service.

Abstract.In this paper the general class V of spline-collocation methods for first order systems of ordinary differential equations is investigated. The methods can in part be regarded as so-called multivalue methods. This type contains the generalized singly-implicit methods treated by Butcher.It is shown here, how any multivalue type representative of V yields a matrix valued function ~u, for the characterization of stability at infinity. It is shown in particular, that the structure of t/, allows us to construct infinity-stable methods by an appropriate choice of the collocation points.

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