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- W3197748215 abstract "This chapter is devoted to the theory of integration introduced by Jaroslav Kurzweil in the form presented in his articles dated 1957, 1958, 1959, and 1962, and so on. It provides the heart of the theory of generalized ordinary differential equations which is precisely the Kurzweil integration theory, presented in a concise form which includes its most fundamental properties–those usually expected that a “good integral” will fulfill. The chapter aims to present a short historical background and its relation with the Kurzweil integral. A common rigid flat pendulum, whose pivot is forced to oscillate along the vertical line, has only one stable point, that is, vertically downwards. Kapitza pendulum is stabilized by minimizing the potential energy. The chapter concludes by calling the reader's attention to the fact that the main feature of the Kurzweil integral is to handle well highly oscillating functions as shown by the Kapitza equation for the inverted pendulum." @default.
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- W3197748215 date "2021-09-03" @default.
- W3197748215 modified "2023-10-16" @default.
- W3197748215 title "The Kurzweil Integral" @default.
- W3197748215 doi "https://doi.org/10.1002/9781119655022.ch2" @default.
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