For now this site only includes links to my master thesis on "State-space representation of convolution terms for surface vessels with forward speed" from 2004, just to make it findable. Also available here
The equations of motion for surface vessels typically use matrices with frequency-varying hydrodynamic coefficients; added mass and damping. Whereas this formulation is able to, for many applications, sufficiently describe the motions of the vessel, it is very inconvenient when used for control purposes. These undesirable properties may make it necessary to adopt complicated schemes to overcome the presented difficulties. Furthermore, this formulation has a mass matrix that is non-symmetric at forward speed.
Time-domain descriptions using memory functions, while accurately describing motion without resorting to frequency-varying coefficients, are not easily modelled using standard simulation tools and requires significant care when used with variable-step solvers. Instead of memory functions, this work uses a state-space model to represent these effects, calculated from the memory function using identification and model reduction.
This thesis proposes a six degrees-of-freedom equation of motion specifically geared towards control synthesis and easy simulation. Up to the accuracy of strip methods, forward speed effects are accounted for in the time-domain description.
The link between frequency-domain and time-domain descriptions are restated, while several practical concerns when implementing this link are investigated with some results of interest when implementing the time-domain description.
One interesting topic of further investigation has been identified. Frequency-domain descriptions of causal, linear systems are required to adhere to the Kramers-Kronig relations, relations that link the real and imaginary part of the force coefficients to each other. These relations are required to hold for the radiation problem, a causal system that is linear in the present description. However, they do not immediately hold for several strip theories, including that of Salvesen, Tuck and Faltinsen.
Finally, the equation of motion is implemented in a six degrees-of-freedom simulator in Matlab/Simulink, with forward speed, using a strip-method like approach.