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.

翻译：本文研究了平面内质点与刚体运动学直至高阶加速度的问题。通过讨论点轨迹，从高阶极点推导出运动平面的高阶布雷斯圆。本文采用向量空间R^2中的辛几何作为新方法，推导出若干新的递归向量公式。谨以此文纪念Pennestri教授。