Recovering modified Newtonian dynamics by changing inertia

Milgrom's modified Newtonian dynamics (MOND) has done a great job on accounting for the rotation curves of a variety of galaxies by assuming that Newtonian dynamics breaks down for extremely low acceleration typically found in the galactic contexts. This breakdown of Newtonian dynamics may be a result of modified gravity or a manifest of modified inertia. The MOND phenomena are derived here based on three general assumptions: 1) Gravitational mass is conserved; 2) Inverse-square law is applicable at large distance; 3) Inertial mass depends on external gravitational fields. These assumptions not only recover the deep-MOND behaviour, the accelerating expansion of the universe is also a result of these assumptions. Then Lagrangian formulae are developed and it is found that the assumed universal acceleration constant a0 is actually slowly varying by a factor no more than 4. This varying 'constant' is just enough to account for the mass-discrepancy presented in bright clusters.