Abstract
The brachistochrone problem posed by Johann Bernoulli was a new type of mathematical problem which required a new mathematical approach. Lagrange developed the calculus of variations in which he considered suboptimal paths nearby the optimal one. He then showed that, for arbitrary but infinitesimal variations from the optimal path, the function sought must obey a differential equation now known as the Euler-Lagrange equation.
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References
A.E. Bryson Jr., Y.C. Ho, Applied Optimal Control (Hemisphere Publishing, Washington, D.C., 1975)
S.J. Citron, Elements of Optimal Control (Holt, Rinehart, and Winston, New York, 1969)
D.T. Greenwood, Classical Dynamics (Dover, New York, 1997)
M.R. Hestenes, Calculus of Variations and Optimal Control Theory (Wiley, New York, 1966)
P. Kenneth, R. McGill, Two-point boundary value problem techniques, in Advances in Control Systems: Theory and Applications, vol. 3, chap. 2, ed. by C.T. Leondes (Academic, New York, 1966)
C. Lanczos, The Variational Principles of Mechanics, 4th edn. (Dover, New York, 1986)
D.A. Pierre, Optimization Theory with Applications (Wiley, New York, 1969)
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Longuski, J.M., Guzmán, J.J., Prussing, J.E. (2014). The Euler-Lagrange Theorem. In: Optimal Control with Aerospace Applications. Space Technology Library, vol 32. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8945-0_3
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DOI: https://doi.org/10.1007/978-1-4614-8945-0_3
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