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SOFIA stands for Stratospheric Observatory for Infrared Astronomy. She says:

My telescope stays stable with a spherical bearing, shock absorbers, and gyroscopes.

I suppose a similar system would work for an optical telescope on a maritime vessel as well. But what about a radio-telescope on a ship with a dish of around 10m? What are arguments (ideally mathematical ones) against a similar construction like for SOFIA?

SOFIA stabilization

References

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You asked for arguments against this, but I don't think there are any other than money. Consider the AN/SPQ-11 passive radar that was aboard the US Navy ship Observation Island. The actual receiver area is not as large (7M according to https://fas.org/irp/program/collect/cobra_judy.htm), but we could imagine a larger antenna being placed on a larger ship such as the USS Enterprise. The beam (maximum width) of the Enterprise is 41 meters, which could certainly accommodate a 10-20m dish.

I think the only reason this would not be built would be lack of funds. From an engineering perspective, it seems doable.

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