A New Approach in Plane Kinematics

TL;DR

This paper introduces a novel approach using symplectic geometry to analyze plane kinematics, focusing on higher-order accelerations, point trajectories, and recursive vector formulas, advancing the theoretical understanding of planar motion.

Contribution

It presents a new symplectic geometric framework for plane kinematics, including recursive vector formulas and higher-order acceleration analysis, which are novel contributions in the field.

Findings

Derived new recursive vector formulas for plane kinematics.

Connected higher-order poles to Bresse circles in the moving plane.

Introduced symplectic geometry as a tool for kinematic analysis.

Abstract

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.