  Using Onsager's variational principle, we derive dynamical equations for a
nonequilibrium active system with odd elasticity. The elimination of the extra
variable that is coupled to the nonequilibrium driving force leads to the
nonreciprocal set of equations for the material coordinates. The obtained
nonreciprocal equations manifest the physical origin of the odd elastic
constants that are proportional to the nonequilibrium force and the friction
coefficients. Our approach offers a systematic and consistent way to derive
nonreciprocal equations for active matter in which the time-reversal symmetry
is broken.
