English Title
A more accurate investigation into brachistochrones
Enestrom Number
759
Fuss Index
381
Original Language
Latin
Content Summary
Euler begins by mentioning how he was not satisfied by his achievements in E42, and now attempts to derive the equations from scratch, using the "first principles" of motion (basically Newton's laws of motion). He first considers the two dimensional brachistochrone problem, finding that v dv = 2g(X dx + Y dy). Subsequently, using his "isoperimetric treatment" (which is basically a more refined Euler-Lagrange equation) he finds Θ=v2/(2gr), where r is the radius of curvature, Θ is the normal force and g is half the gravitational acceleration. After this, Euler examines the three-dimensional brachistochrone problem.
Published as
Journal article
Published Date
1822
Written Date
1780
Original Source Citation
Mémoires de l'académie des sciences de St.-Petersbourg, Volume 8, pp. 17-28.
Opera Omnia Citation
Series 1, Volume 25, pp.314-325.
Record Created
2018-09-25
