Talk 9

Title:  About Lindow’s Article “Ein Spezialfall des Vierkörperproblems” (1921): Historical Interpretation and Analytical Reconstruction of a Special Case of the Four-Body Problem

Speaker:  Gersonilo Oliveira

Affiliation: Universidade Federal do Agreste de Pernambuco (UFAPE)

Abstract: This talk focuses on a detailed analysis of the internal structure of Martin Lindow’s article “Ein Spezialfall des Vierkörperproblems” (1921). We examine how Lindow organizes his study of the system formed by three equal masses in rotation and a fourth infinitesimal mass, highlighting the geometric coherence, the deductive methods, and the formulation of energy surfaces and equilibrium points.

   A second axis of the presentation is the theoretical contextualization of Celestial Mechanics literature at the beginning of the 20th century. Lindow writes at a transitional moment between the Lagrangian–Newtonian tradition — structured by Hill, Tisserand, and Poincaré — and the rise of a more analytical approach focused on the qualitative study of Hamiltonian systems, stability, and energy curves.

    Finally, the presentation emphasizes the article’s central innovation: the application of Weierstrass elliptic functions to regularize the system and describe behavior near singularities. This procedure, rare in the literature of the time, anticipates the modern use of complex-analytic tools to treat collisions, forbidden regions, and orbital transitions in problems with symmetry.

      With these three axes—structure, theoretical context, and analytical innovation—the talk aims to show Lindow’s relevance within the history of celestial mechanics and his distinctive contribution to the study of the four-body problem.