What Makes the Secular Equation Secular in Normal Mode Analysis?

[nnj]

When looking for frequencies of normal modes in coupled oscillators, one can obtain a so-called secular equation given enough information.

Why call this a secular equation? What is secular about it?

 

[nasu]

It seems that one of the first (or common) use of this kind of equation was to the description of the long period perturbations in planetary motions. So here secular refers to long time periods, ages, etc.

Similar root for the "secular" meaning non-religious. God and the sacred things were considered outside of time so the "secular" business was related to the temporary, time-related world. (the "civil", outside the church, authorities were also called "temporal").

Secular is related now to the 100 year period (in romance languages) but it used to be more general, referring to any long period or generation.

 

[boneh3ad]

In terms of normal modes, in perturbation theory, secular terms are those that are found in the higher-order solutions that solve the order unity differential equation.