A New Approach in Plane Kinematics

2026-02-13

Technology Category

• Intelligent Robots: Motion and Path Planning
• Planning, Routing, and Scheduling: Activity and Plan Recognition
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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.

Problem

• plane kinematics
• higher-order accelerations
• point trajectories
• Bresse circles
• rigid bodies

Innovation

• symplectic geometry
• higher-order accelerations
• recursive vector formulas
• Bresse circles
• plane kinematics