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In this chapter, we try to reconstruct the history of the Principle of Virtual Work (PVW) in mechanics to find its original formulation. This task is not pursued because of its intrinsic interest only. Actually, when we intend to formulate new models in the mechanics of metamaterials for instance, we need to understand which is now and was in the past the most powerful conceptual tool that favors innovation and creativity in the conception of novel mathematical models. We believe that giving evidence about the historical priority of the PVW will help to establish an agreement among today’s and future researchers in mechanical sciences about the most suitable methodology to be used. Another important question that we will address in this chapter regards the origin of the concept of kinematics as distinguished from the one of dynamics. The birth of dynamics, obviously, is a consequence of the formulation of a principle from which one can deduce the algorithm that allows, for a given physical system, the prediction of the actual motion over time among those chosen as admissible by the preliminary kinematic study. It is well-established that the formulation of the Principle of Virtual Velocities (later called Principle of Virtual Work) is already present in the Greek textbook Mechanica Problemata (The Mechanica Problemata) which surely precedes the works by Hipparchus and Seleucus of Seleucia credited to be the inventors of dynamics. Moreover, the known later texts by Archimedes give the first known examples of the postulation of mechanics based on Balance Laws: we, therefore, conjecture that the first Principle used for formulating Dynamics was exactly the Principle of Virtual Velocities. Using logical methods, the philological work of the many scholars who studied Mechanica Problemata before us, and carefully exploiting the basic ideas on which Mechanics is founded, we conjecture the original ancient formulation of the PVW as reconstructed from our fragmentary sources. We also conjecture that this formulation was due to Archytas of Tarentum and his early successors.

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Who Was the First to Formulate the Principle of Virtual Work?

  • 章节

  • 发表日期：

    2025年

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  • Francesco dell’isola,
  • Maximilian Stilz,
  • Mario Spagnuolo

摘要

In this chapter, we try to reconstruct the history of the Principle of Virtual Work (PVW) in mechanics to find its original formulation. This task is not pursued because of its intrinsic interest only. Actually, when we intend to formulate new models in the mechanics of metamaterials for instance, we need to understand which is now and was in the past the most powerful conceptual tool that favors innovation and creativity in the conception of novel mathematical models. We believe that giving evidence about the historical priority of the PVW will help to establish an agreement among today’s and future researchers in mechanical sciences about the most suitable methodology to be used. Another important question that we will address in this chapter regards the origin of the concept of kinematics as distinguished from the one of dynamics. The birth of dynamics, obviously, is a consequence of the formulation of a principle from which one can deduce the algorithm that allows, for a given physical system, the prediction of the actual motion over time among those chosen as admissible by the preliminary kinematic study. It is well-established that the formulation of the Principle of Virtual Velocities (later called Principle of Virtual Work) is already present in the Greek textbook Mechanica Problemata (The Mechanica Problemata) which surely precedes the works by Hipparchus and Seleucus of Seleucia credited to be the inventors of dynamics. Moreover, the known later texts by Archimedes give the first known examples of the postulation of mechanics based on Balance Laws: we, therefore, conjecture that the first Principle used for formulating Dynamics was exactly the Principle of Virtual Velocities. Using logical methods, the philological work of the many scholars who studied Mechanica Problemata before us, and carefully exploiting the basic ideas on which Mechanics is founded, we conjecture the original ancient formulation of the PVW as reconstructed from our fragmentary sources. We also conjecture that this formulation was due to Archytas of Tarentum and his early successors.