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(2013) Calculus of variations, applied mathematics, and physics/Variationsrechnung, angewandte mathematik und physik, Dordrecht, Springer.
Zermelo treats the problem of motion of a string in a potential field W with the help of Hamilton's principle. A string is an elastic physical body with small cross section. It can be represented by a continuous curve r = r(t) = (x(t), y(t), z(t)) that can assume every possible position. A string is therefore completely flexible, but by assumption inextensible. For inextensible strings that are fixed at both ends, the equations of motion (the Euler equations) become L = (T − U) + λ(S − 1). The Lagrange multiplier λ can be physically interpreted as the tension of the string.
Publication details
DOI: 10.1007/978-3-540-70856-8_5
Full citation:
Thiele, R. (2013). Introductory note to s1899b, in Calculus of variations, applied mathematics, and physics/Variationsrechnung, angewandte mathematik und physik, Dordrecht, Springer, pp. 280-285.
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