An alternative stability analysis technique for the simplest walker

摘要

We revisit the simplest walker studied earlier by Garcia and co-workers. We extend the small-slope stability analysis to second order, substantially improving accuracy, and also provide some details left out of the earlier work. We develop an alternative (reverse) approach for the stability analysis, which involves shorter calculations: for stability analysis upto any given order, the new procedure requires calculations to one order less than the previous (forward) procedure. The stability results obtained by the two methods are, nevertheless, equivalent. [References: 8]