Abstract

The Gibbs-Appell formulation, a powerful approach in analytical mechanics, has undergone significant advancements in recent years, particularly in its application to variable mass systems and non-material volumes. This mini-review traces the historical development of the Gibbs-Appell approach, from its inception in classical mechanics to its modern extensions. We highlight the formulation’s unique advantages in handling complex dynamic systems, especially those with changing mass and fluidstructure interactions. Key benefits include simplified equations for constrained systems, efficient handling of non-holonomic constraints and improved computational stability for variable mass problems. Recent applications in robotics, aerospace engineering and fluid dynamics demonstrate the formulation’s versatility and effectiveness. The paper concludes by discussing future directions, emphasizing the potential for further integration with machine learning techniques and expansion into multi-physics simulations. As the Gibbs-Appell approach continues to evolve, it promises to enhance our ability to model and control increasingly complex dynamic systems, contributing to advancements in robotics, artificial intelligence and computational physics.