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Full-Text Articles in Physical Sciences and Mathematics
Euler's Navigation Variational Problem, Sylvio R. Bistafa
Euler's Navigation Variational Problem, Sylvio R. Bistafa
Euleriana
In a 1747 publication, De motu cymbarum remis propulsarum in fluviis (“On the motion of boats propelled by oars in rivers”), Leonhard Euler (1707-1783) works out various instances of a boat moving at constant speed across a stream flowing in straight streamlines at assigned speeds, in which one of these gives rise to a variational problem consisting of finding the quickest crossing path between two points on opposite side of the river banks, which is generally known as the navigation variational problem. This problem together with the well-known catenary and brachistochrone problems, are considered classical examples in the calculus …
On The Motion Of Boats Propelled By Oars In Rivers, Sylvio R. Bistafa
On The Motion Of Boats Propelled By Oars In Rivers, Sylvio R. Bistafa
Euleriana
Euler considers the following problem: A boat with a perfect rudder moves at constant speed across a stream flowing in straight streamlines 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.)