- #1
Deiniol
- 4
- 0
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 to:
\begin{equation}
u=u_0+u_1\cos(n\sigma_rt-\phi_1) + u_1'\cos([n+\beta]\sigma_rt-\phi_1')+\ldots
\end{equation}
where β=±1 and n is an integer. I don't follow the manipulation from the first equation to the other, I just wondered if anyone is familiar with this trick and might be able to talk me through it. Many thanks.
\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 to:
\begin{equation}
u=u_0+u_1\cos(n\sigma_rt-\phi_1) + u_1'\cos([n+\beta]\sigma_rt-\phi_1')+\ldots
\end{equation}
where β=±1 and n is an integer. I don't follow the manipulation from the first equation to the other, I just wondered if anyone is familiar with this trick and might be able to talk me through it. Many thanks.