  Mechanical systems, in nature, are often described by a set of
continuous-time, nonlinear, second-order differential equations (SODEs). This
has motivated designs of various control laws implemented on digital
controllers, consequently requiring numerical discretization schemes. Feedback
linearizability of such sampled systems depends on the discretization scheme or
map choice. In this article, we utilize retraction maps and their lifts to
construct feedback linearizable discretizations for SODEs, which can be applied
to various mechanical systems.
