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Some special cases seem easy:

- interaction by a rigid rod

- any interaction, but the field and interaction forces "decoupled" (example: two spring-connected bodies of equal mass in a constant field: oscillation and acceleration by the external field take place independently)

A non trivial case:

- two spring-connected masses in a gravitational field

What I find especially hard to model in this case is the rigidness of the spring perpendicular to the connecting line (which I feel necessary to presuppose somehow).

Can anyone give me some hints under which general conditions on the interaction and the external forces the problem has a closed solution - and where I might find an elaborate treatment of the case of two spring-connected masses in a gravitational field.

Many thanks in advance

Hans