I have read some of the history of John Harrison's marine chronometers and have found it fascinating. I would like to deepen my understanding of Harrison's amazing inventions by learning more about how they actually worked, but I have had trouble finding sufficiently detailed descriptions, let alone analyses of why they work.
To give some idea of what I'm looking for, let's consider the design now known as H1. As I understand it, the crucial component consisted of two dumbbell-shaped rods, each pivoting about its own center and connected to each other by two springs. I believe that the main point—and here is where I'm speculating because I haven't actually done the calculations—is that the period of oscillation of this mechanism is relatively robust to impulses. More precisely, some things that I have read seem to suggest that the mechanism is particularly robust to impulses that lie in the plane of the two dumbbells, but that its main weakness is that it is not as robust to impulses in the direction perpendicular to this plane. Assuming that this is roughly correct, what I would ideally like to see is a series of exercises (of the type one might see in a course in advanced classical mechanics) that walk you through the relevant calculations and let you quantify the effect of various impulses.
In the case of H1, I might be able to flesh out the preceding paragraph myself, but for the other designs, particularly the famous H4 design, I have not been able to find sufficiently detailed descriptions of the mechanism to even begin to understand them at the level that I would like. Note: I recognize that some of Harrison's innovations concerned robustness to temperature variations, by the use of things like bimetallic strips. Personally, I'm less interested in that kind of thing (even though they are obviously extremely important in practice) than in the rigid-body mechanics of balance wheels, escapements, etc., and in particular the analysis of why they are (or are not) robust to the conditions on a moving ship.
Is there any account out there that addresses what I'm asking for?