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Bernoulli’s light ray solution of the brachistochrone problem through Hamilton’s eyes. (English) Zbl 1300.01014


MSC:

01A45 History of mathematics in the 17th century
78A05 Geometric optics
49-03 History of calculus of variations and optimal control
49K15 Optimality conditions for problems involving ordinary differential equations
47J30 Variational methods involving nonlinear operators

Biographic References:

Bernoulli, Johann; Hamilton, William Rowan
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References:

[1] DOI: 10.1007/978-1-4757-2063-1
[2] DOI: 10.1007/978-94-011-3330-2
[3] Bernoulli J., Johannis Bernoulli (1742)
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[5] Broer H. W., Euclides 70 pp 110– (1995)
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[7] do Carmo M. P., Differential Geometry of Curves and Surfaces (1976) · Zbl 0326.53001
[8] Euler L., Leonhardi Euleri Opera Omnia 72 (1975) · Zbl 0183.00501
[9] Feynman R. P., The Feynman Lectures on Physics 1 (1965) · Zbl 0138.43404
[10] Goldstein H., Classical Mechanics (1980)
[11] DOI: 10.1007/978-1-4613-8106-8
[12] DOI: 10.1090/surv/014
[13] Hamilton W. R., Trans. Roy. Irish Acad. 15 pp 69– (1828)
[14] DOI: 10.1098/rstl.1834.0017
[15] DOI: 10.1098/rstl.1835.0009
[16] Hart K. P., Pythagoras 39 (2000)
[17] Lagrange J. L., Mécanique Analytique 2
[18] Leonhardt U., Geometry and Light: The Science of Invisibility (2010)
[19] Poston T., Catastrophe Theory and Its Applications (1978) · Zbl 0382.58006
[20] Shafer D. G., MATerials MATemàtics 5 (2007)
[21] van Maanen J. A., Een Complexe Grootheid, Leven en Werk van Johann Bernoulli 1667–1748 34 (1995)
[22] Weierstraß K., C.G.J. Jacobi’s Gesammelte Werke (1891)
[23] Yoder J. G., Unrolling Time (1988) · Zbl 0687.01005
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