E86 -- De motu corporum in superficiebus mobilibus

(On the movement of bodies on movable surfaces)

(based on C. Truesdell's An idiot's fugitive essays on science: methods, criticisms, training, circumstances)
Euler looks at the motion of bodies that are constrained to move on a rigid curve that is either in free or rigid motion. Note that E826, E827, E828, and E829 all contain his earlier treatments of special cases of this problem. In this current paper, he uses a mathematically complex principle that is general in principle to solve some extremely difficult cases of this problem. For example, he solves the problem when a particle is free to move within a curved tube that is free in space. In addition, he foreshadows his theory of rigid bodies by looking at the case of a particle that is free to move in a tube that is given an assigned motion.

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