An annotated translation from Latin of L. Euler's 'On the motion of boats propelled by oars in rivers'

TL;DR

This paper provides an annotated Latin translation of Euler's work on the problem of steering a boat across a flowing stream, including detailed analysis of specific cases and a variational problem formulation.

Contribution

It offers a detailed translation and interpretation of Euler's original work on boat motion in streams, highlighting the mathematical approach and variational problem involved.

Findings

Euler's analysis of boat steering in flowing streams

Derivation of specific solutions for different stream conditions

Formulation of a variational problem for optimal navigation

Abstract

Euler considers the following problem: A boat with a perfect rudder moves at constant speed across a stream flowing in straight fillets at assigned speeds. Assuming that the downstream velocity of the boat equals that of the river, how should the rudder be set so that the boat traverses a given path? He works out various instances, one of which gives rise to a variational problem, in detail. (From Clifford Truesdell's An idiot's fugitive essays on science: methods, criticisms, training, circumstances.)