In the absence of work on the system, is there a closed form equation for the motion of a set of constrained rigid bodies (let's say, using Revolute (ie: simple pivot) constraints)?
If the bodies are fixed to the ground and subject to gravity, there definitely isn't. For instance, the double pendulum. But if no work is being done (ie: there are no non-constraint forces) does the motion allow a closed form? If so, how do you find it given the initial velocities and configuration of the system?
The center of mass of the system would have a linear velocity, for instance, as a consequence of Newton's second law. But the individual bodes themselves could have some very twisty motions.
I'm thinking it would have a form similar to the forward kinematics equation for a robot arm. That has the form $[\Theta_1] * (r_1 + [\Theta_2] * (r_2 + \ldots))$, where $r_i$ is the displacement from one link to the next and $[\Theta_i]$ is the rotation transform of a certain link.
EDIT: as an example, consider something like:
Are the motions of the central body and all the little pendulums expressible in a closed form assuming there's no gravity or motors or anything?