  Floating offshore structures often exhibit low-frequency oscillatory motions
in the horizontal plane, with amplitudes in the same order as their
characteristic dimensions and larger than the corresponding wave-frequency
responses, making the traditional formulations in an inertial coordinate system
inconsistent and less applicable. To address this issue, we extend and explore
an alternative formulation completely based on a non-inertial body-fixed
coordinate system. Unlike the traditional seakeeping models, this formulation
consistently allows for large-amplitude horizontal motions. A numerical model
based on a higher-order boundary element is applied to solve the resulting
boundary-value problems in the time domain. A recently developed new set of
explicit time-integration methods, which do not necessitate the use of upwind
schemes for spatial derivatives, are adopted to deal with the convective-type
free-surface conditions. To suppress the weak saw-tooth instabilities on the
free surface in time marching, we also present novel low-pass filters based on
optimized weighted-least-squares, which are in principle applicable for both
structured and unstructured meshes. The presented schemes for the convection
equation and the low-pass filter are also relevant for other engineering fields
dealing with similar mathematical problems. For ship seakeeping and added
resistance analyses, we show that the present computational model does not need
to use soft-springs for surge and sway, in contrast to the traditional models.
For a floating monopile, the importance of consistently taking into account the
effects of large horizontal motions is demonstrated considering the
bi-chromatic incident waves. The present model is considered as a complete 2nd
order wave-load model, as all the 2nd order wave loads, including the
sum-frequency and difference-frequency components, are solved simultaneously.
