On the movement of a boat with oars propelled through running waters
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. (Based on Clifford Truesdell's An idiot's fugitive essays on science: methods, criticisms, training, circumstances.)
Original Source Citation
Commentarii academiae scientiarum Petropolitanae, Volume 10, pp. 22-39.
Opera Omnia Citation
Series 2, Volume 20, pp.83-100.