The “Theoretical dynamics” group led by Theodore Vogel (1903-78) at the Centre de Recherche en Physique (Marseilles, France), after 1948 has yet drawn only little attention regarding the history of “non linear sciences”. Its contributions are but original and interesting raising the question of the interplay between the evolution of mathematics of dynamical systems and analog computing.
Vogel was an electrical engineer who got into research in physics and mathematical-physics after 1947. He produced many studies, theoretical, mathematical and experimental, concerning the dynamics of systems : non linear oscillations, surging of waves, aging of systems... He founded his group by attracting engineers and physicists, turned to mathematical and theoretical research, but maintaining their ability with experiments and practical numerical calculations. He was a promoter of “mathematics for the engineer” in his lab. His “Theoretical dynamics” group grew at its zenith in 1964 dealing constantly with one constraint : due to financial and institutional reasons, no computer, neither analog nor digital were available in the lab until1964.
Facing international competition with computer-aided groups, Vogel encouraged his colleagues on the way to developping their own analog devices to deal with calculations, fitted to their specifc dynamical systems.
Through this case study, we investigate this original program of research at the crossroad of mathematics and analog computing. We explain how this practice articulate the development of mechanical and electronic systems to render solutions of equations, with the mathematics of differential equations and dynamical systems. We emphasize the role of analogies in this practice as a mean to compare dynamical systems of different nature, and as a mean to conceive specific calculating instruments. These instruments were intended to render phase portraits of dynamical systems necessary to their geometrical and topological analysis. We must stress the importance given to numerical results and graphical rendering of solutions, to image and numbers in their practice. It is all supported by a clearly anti-bourbakist epistemology, advocated by Vogel following his conceptions on mathematics and their relation to experiments.
We conclude with a few words on the development of the department of “Applied mathematics”, which can be seen as the heritage of this group, after the retirement of Vogel.