arXiv subjects
Publications and source records attributed to Stefan Goessner.
The kinematics of particles and rigid bodies in the plane are investigated up to higher-order accelerations. Discussion of point trajectories leads from higher-order poles to higher-order Bresse circles of the moving plane. Symplectic geometry in vector space R^2 is used here as a new approach and leads to some new recursive vector formulas. This article is dedicated to the memory of Professor Pennestri.
In this follow-up article to Symplectification of Circular Arcs and Arc Splines, biarc geometry is examined from a purely geometric point of view. Two given points together with their associated tangent vectors in the plane are sufficient to define two directed, consecutive circular arcs. However, there remains one degree of freedom to determine the join point of both arcs. There are various approaches to this in the literature. A novel one is presented here.
The mathematical theory underlying Hamiltonian mechanics is called symplectic geometry. So symplectic geometry arose from the roots of mechanics and is seen as one of the most valuable links between physics and mathematics today. Symplectic geometry in its simplest possible case is the geometry of the plane. Surprise is, we can hardly find relevant publications regarding that simple 2D case. Primary goal of this paper is to discuss the suitability of symplectic geometry in the plane for solving standard geometric and mechanical problems in physics and engineering education.