Relations between Variational Problems in Time Domain and Those in Frequency Domain : Applications to the Theory of a Floating Body

Abstract

Theories of a floating body are usually dealt with in "frequency domain", and it may be said that relations between "time domain" and "frequency domain" have not been clarified sufficiently. For an example, variational problems which is equivalent to the boundary value problems in frequency domain may be derived, but their relations to the Hamilton principle in time domain are not clear enough. In the present paper, these problems are discussed using a one dimensional oscillator, and variational problems in frequency domain are derived as Fourier transforms of variational problems in time domain. A new variational problem in time domain, which is different from Hamilton's principle, are derived. Applications to the theory of a floating body are also discussed sufficiently.