Article ID: CBB001211762

Leonhard Euler's Early Lunar Theories 1725--1752: Part 2: Developing the Methods, 1730--1744 (2013)

unapi

The analysis of unpublished manuscripts and of the published textbook on mechanics written between about 1730 and 1744 by Euler reveals the invention, application, and establishment of important physical and mathematical principles and procedures. They became central ingredients of an embryonic lunar theory that he developed in 1744/1745. The increasing use of equations of motion, although still parametrized by length, became a standard procedure. The principle of the transference of forces was established to set up such equations. Trigonometric series expansions together with the method of undetermined coefficients were introduced to solve these equations approximatively. These insights constitute the milestones achieved in this phase of research, which thus may be characterized as developing the methods. The documents reveal the problems Euler was confronted with when setting up the equations of motion. They show why and where he was forced to introduce trigonometric functions and their series expansions into lunar theory. Furthermore, they prove Euler's early recognition and formulation of the variability of the orbital elements by differential equations, which he previously anticipated with the concept of the osculating ellipse. One may conclude that by 1744 almost all components needed for a technically mature and successful lunar theory were available to Euler.

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Authors & Contributors
Ferraro, Giovanni
Verdun, Andreas
Panda, Sudhira
Sznajder, Roman
Dora Musielak
Franz Lemmermeyer
Concepts
Mathematics
Celestial mechanics
Physics
Astronomy
Manuscripts
Lunar theory
Time Periods
18th century
Medieval
Enlightenment
Ancient
16th century
Places
Switzerland
Russia
Poland
Greece
India
Great Britain
Institutions
St. Petersburg Academy of Sciences
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