relationship between contact model acceleration term 'a_0` and classical acceleration

[bilal-bdai]

for writing the contact model we have
$$
J \ddot{q} + \dot{J} \dot{q} = a_{spatial}
$$
what's the explanation for writing $a^{classical}{linear} = \dot{J}{linear} \dot{q}$ here

I tried to write it down but i can't seem to make the connection

[cmastalli]

Hi @bilal-bdai,

This constraint imposes contact accelerations equal to zero. However, spatial acceleration is a property of a body as a whole, not of a body-fixed point. Indeed, we are interested in constraining the classical acceleration, not the spatial acceleration. Moreover, we are considering its linear part only as this is a 3D contact model.

Note that we also include the Baumgarte stabilization terms in a0.