Models of a modified-inertia formulation of MOND

Models of "modified-inertia" formulation MOND are described and applied to nonrelativistic many-body systems. They involve time-nonlocal equations motion. Momentum, angular momentum, energy (nonlocally) defined, whose total values conserved for isolated The models make all the salient predictions. Yet, they differ from existing "modified-gravity" formulations in some second-tier describe correctly motion a composite body low-acceleration field even when internal accelerations its constituents high. exhibit external effect (EFE) that shows important differences what we have come expect modified-gravity versions: In one, simple example models, determines EFE, case dominant field, is $\mu(\theta\langle a_{ex}\rangle/a_0)$, where $\mu(x)$ `interpolating function' describes rotation curves, compared with $\mu(a_{ex}/a_0)$ presently-known formulations. two main while $a_{ex}$ momentary value acceleration, $\langle a_{ex}\rangle$ certain time average it, $\theta>1$ an extra factor depends on frequency ratio external- internal-field variations. Only ratios frequencies enter, $a_0$ remains only new dimensioned constant. For system circular orbit galaxy (such as vertical dynamics disc galaxy), first difference disappears, since a_{ex}\rangle=a_{ex}$. But $\theta$ can appreciably enhance EFE quenching effects, over deduced modified gravity. Some exact solutions also described, such harmonic force, general, two-body problem, which deep-MOND regime reduces single-body problem.