Techniques for the solution of linear matrix differential equations have previously been applied to the dynamic analysis of a mechanism. However, because the mechanism changes geometry as it rotates, a large number of solutions are necessary to predict the mechanism’s elastic behavior for even a few revolutions. Also, a designer is frequently concerned with the elastic behavior of only one point on the mechanism and has no practical interest in a complete solution. For these reasons, a method is given here for reducing the total number of coordinates to one coordinate at the point of design interest. A considerable saving in computational time is obtained since the dynamic solution involves one degree of freedom instead of many. Further, since any solution will make use of some limiting assumptions, results here indicate that, for design purposes, reducing the coordinates does not significantly affect comparable accuracy.
A Matrix Differential Harnack Estimate for a Class of Ultraparabolic Equations
