Thanks for the reply Erland. The reason for the change is to eventually get u(x,t)|u(x,t)| into a form suitable for a Fourier expansion. I think that by letting θ=σt-Φ1 and α=σrt+Φ1-Φ1' where σr=σ-σ' to transform (1) in the OP to:
\begin{equation}...
Hi there, I am reading through a thesis and the author takes the infinite series:
\begin{equation}
u(x,t)=u_0(x)+u_1(x)\cos(\sigma t - \phi_1(x)) + u_1'(x)\cos(\sigma' t - \phi'_1(x))+\ldots
\end{equation}
and by letting σr be the difference between the frequencies σ and σ' changes the above...
Am working through the link now, I find frames of reference hard to visualise. Would my statement be correct in frame of reference located at the centre of mass? I get the gradient of the gravitational force explanation. I can follow the mathematics of it but when I am asked why is there a bulge...
Sorry to bump this thread though it better than starting a new one. At the risk of sounding daft, would it be correct to explain the two tidal bulges on either side of a water world in terms of the vector sum of the attractive gravitational force of the Moon and the centrifugal force acting in...