The first experiment is to examine the action/reaction influence on hinge horizontal position. It uses a 2D mass-spring simulation with a grid of equal masses arranged in a rectangular lattice as a crude approximation to the upper block. The masses are connected to nearest neighbors in both dimensions by translational springs and rotational springs are supplied at each mass node. No regard is given for the scale of mass, only for the length dimension and the distribution of mass. The lower left corner of the block (or sheet) is constrained against translation so that it acts as a hinge, while the sheet is allowed to rotate about the corner point under the influence of gravity and optional supporting force (ensemble). Time begins with a level upper block being released.
Two types of trials are conducted:
1) The hinge is constrained against translation in both the x
2) The hinge is constrained against translation in only the y
Both cases allow free rotation about the hinge point, any retarding moment is supplied by optional support forces, if any. In this model, there is no lower section. The attribute of providing a hinge, either fixed or free to move horizontally, is supplied by way of a constraint rule on the solver. The attribute of support or more generally resistance to motion is supplied by external forces defined to act on a point in a particular direction, which need not be constant.
The first set of experiments omit external forces except gravity. This is the most elementary starting point but also leads to large angular acceleration, so there's no need to run long to see what's happening. The gravity-only sims run for one second.
The arrangement at t=t0 and t=1s is shown in the images below:
The model shown here is 'weak' in terms of ratio of spring constant to density. The purpose was to exaggerate the distribution of stress (color) experienced by the sheet as it rotated freely about the hinge and to be a graphic reminder that, in this first series of simulations, the upper block is pretty stiff, but it is by no means rigid. Subsequent models generating the data presented next were stiffened up considerably from this example but do display multi-modal oscillation. No damping is used, except as otherwise noted.
Future simulations will include truly rigid bodies, among other things.