the solenoidal field ${{\bf S}}$ has been shown to be small for some configurations (Brada & Milgrom 1995; Ciotti, Londrillo & Nipoti 2006, hereafter CLN), neglecting it when simulating time-dependent dynamical processes has dramatic effects such as non-conservation of total linear momentum (e.g. Felten 1984; see also Section \[secic\]).

Nowadays several astronomical observational data appear consistent with the MOND hypothesis (see, e.g., Milgrom 2002; Sanders & McGaugh 2002). In addition, Bekenstein (2004) recently proposed a relativistic version of MOND (Tensor-Vector-Scalar theory, TeVeS), making it an interesting alternative to the cold dark matter paradigm. However, dynamical processes in MOND have been investigated very little so far, mainly due to difficulties posed by the non-linearity of equation (\[eqMOND\]). Here we recall the spherically symmetric simulations (in which ${{\bf S}}=0$) of gaseous collapse in MOND by Stachniewicz & Kutschera (2005) and Nusser & Pointecouteau (2006). The only genuine three-dimensional MOND N-body simulations (in which equation \[\[eqMOND\]\] is solved exactly) are those by Brada & Milgrom (1999, 2000), who studied the stability of disk galaxies and the external field effect, and those of Tiret & Combes (2007). Other attempts to study MOND dynamical processes have been conducted using three-dimensional N-body codes by arbitrarily setting 